25:
1618:. The role of the additional fundamental meson superfield M in the dual theory is very crucial in matching the anomalies. The global gravitational anomalies also match up as the parity of the number of chiral fields is the same in both theories. The R-charge of the Weyl fermion in a chiral superfield is one less than the R-charge of the superfield. The R-charge of a gaugino is +1.
1291:
1559:), while in the magnetic theory it is a fundamental field. In both theories the baryons are constructed from quarks, but the number of quarks in one baryon is the rank of the gauge group, which differs in the two dual theories.
780:
657:
1155:
1410:
1023:
369:
2549:
2467:
898:
2218:
2134:
1478:
2052:
1879:
2612:
1806:
1746:
1686:
416:
287:
529:
1979:
1929:
1557:
2385:
2341:
2299:
476:
2702:
Whether
Seiberg duality exists in 3-dimensional nonabelian gauge theories with only 4 supercharges is not known, although it is conjectured in some special cases with
2257:
2671:, for the electric and the magnetic phase. The identification gives rise to complicated integral identities which have been studied in the mathematical literature.
2660:
2636:
2984:
1161:
421:
The dual theory contains a fundamental "meson" chiral superfield M which is color neutral but transforms as a bifundamental under the flavor symmetries.
1566:
of the theories do not agree, which is not problematic as the gauge symmetry is a feature of the formulation and not of the fundamental physics. The
663:
540:
295:
A stronger version of the duality relates not only the chiral limit but also the full deformation space of the theory. In the special case in which
1031:
1488:
Being an S-duality, Seiberg duality relates the strong coupling regime with the weak coupling regime, and interchanges chromoelectric fields (
1301:
904:
1497:
108:
301:
2473:
2391:
2783:(2009). "Applications of the Superconformal Index for Protected Operators and q-Hypergeometric Identities to N=1 Dual Theories".
42:
791:
2989:
2140:
2058:
89:
2999:
46:
1423:
61:
2667:
Another evidence for
Seiberg duality comes from identifying the superconformal index, which is a generalization of the
68:
1610:
Six nontrivial anomalies may be computed on both sides of the duality, and they agree as they must in accordance with
379:
161:
2843:(2000). "Supergravity and a confining gauge theory: Duality cascades and chi SB resolution of naked singularities".
1615:
1509:
200:
2687:
are also gauged. The simplest of these is a super QCD with the flavor group gauged and an additional term in the
35:
2994:
1596:
75:
1987:
1814:
2703:
2979:
57:
2959:
2557:
375:
1752:
1692:
1640:
385:
246:
2915:
2862:
2802:
2745:
482:
122:
1935:
1885:
1526:
2349:
2305:
2263:
2931:
2905:
2878:
2852:
2818:
2792:
2761:
2735:
1505:
150:
1611:
442:
2696:
2226:
1523:
are preserved by the duality. However, in the electric theory the meson is a quark bilinear (
203:
141:. The two theories are not identical, but they agree at low energies. More precisely under a
82:
2923:
2870:
2810:
2753:
1570:
relate distinct physical configurations, and so they need to agree in any dual description.
196:
154:
1492:) with chromomagnetic fields (gluons of the dual gauge group), and chromoelectric charges (
2684:
1567:
211:
142:
2927:
2919:
2874:
2866:
2806:
2749:
2679:
Seiberg duality has been generalized in many directions. One generalization applies to
2642:
2618:
2840:
2723:
2691:. It leads to a series of Seiberg dualities known as a duality cascade, introduced by
2688:
2680:
1563:
1418:
1286:{\displaystyle {\tilde {Q^{c}}}\,({\overline {N_{f}}},1)_{1/(N_{f}-N_{c}),N_{c}/N_{f}}}
177:
146:
130:
2973:
2963:
2836:
2757:
2692:
1592:
165:
2935:
2822:
2814:
2765:
2882:
2726:(1995). "Electric - magnetic duality in supersymmetric nonAbelian gauge theories".
2668:
1579:
157:
2780:
1501:
189:
24:
775:{\displaystyle SU(N_{f})_{L}\times SU(N_{f})_{R}\times U(1)_{B}\times U(1)_{R}}
652:{\displaystyle SU(N_{f})_{L}\times SU(N_{f})_{R}\times U(1)_{B}\times U(1)_{R}}
1150:{\displaystyle Q^{c}\,(1,{\overline {N_{f}}})_{-1/N_{c},(N_{f}-N_{c})/N_{f}}}
1604:
215:
138:
134:
1585:
The global symmetries agree, as do the charges of the mesons and baryons.
2896:
Aharony, O.; Bergman, O.; Jafferis, D.L. (2008). "Fractional M2-branes".
2953:
2857:
2740:
1600:
1405:{\displaystyle M\,(N_{f},{\overline {N_{f}}})_{0,2(N_{f}-N_{c})/N_{f}}}
2954:
Electric-Magnetic
Duality in Supersymmetric Non-Abelian Gauge Theories
1018:{\displaystyle {\tilde {Q}}\,(1,N_{f})_{-1/(N_{f}-N_{c}),N_{c}/N_{f}}}
1520:
2910:
2797:
1516:
1493:
1489:
1588:
In certain cases it reduces to ordinary electromagnetic duality.
18:
16:
Renormalization group duality in supersymmetric gauge theories
364:{\displaystyle {1 \over 3}N_{f}<N_{c}<{2 \over 3}N_{f}}
2544:{\displaystyle -2{\frac {N_{c}^{4}}{N_{f}^{2}}}+N_{c}^{2}-1}
2462:{\displaystyle -2{\frac {N_{c}^{4}}{N_{f}^{2}}}+N_{c}^{2}-1}
893:{\displaystyle Q\,(N_{f},1)_{1/N_{c},(N_{f}-N_{c})/N_{f}}}
2213:{\displaystyle {\frac {-N_{c}^{2}}{N_{f}}}d^{(2)}(N_{f})}
2129:{\displaystyle -{\frac {N_{c}^{2}}{N_{f}}}d^{(2)}(N_{f})}
1607:
which is conjectured to preserve the universality class.
1473:{\displaystyle W=\alpha M{\tilde {Q^{c}}}{\tilde {Q}}}
2645:
2621:
2560:
2476:
2394:
2352:
2308:
2266:
2229:
2143:
2061:
1990:
1938:
1888:
1817:
1755:
1695:
1643:
1529:
1426:
1304:
1164:
1034:
907:
794:
666:
543:
485:
445:
388:
304:
249:
1620:
423:
49:. Unsourced material may be challenged and removed.
2654:
2630:
2606:
2543:
2461:
2379:
2335:
2293:
2251:
2212:
2128:
2046:
1973:
1923:
1873:
1800:
1740:
1680:
1551:
1472:
1404:
1285:
1149:
1017:
892:
774:
651:
523:
470:
418:where R is the R-charge. This is an exact result.
410:
363:
281:
1484:Relations between the original and dual theories
374:the IR fixed point is a nontrivial interacting
164:in N=4 theories and electromagnetic duality in
8:
1603:. There it is realized as the motion of an
214:chiral multiplets in the chiral limit (no
2909:
2856:
2796:
2739:
2644:
2620:
2598:
2579:
2574:
2559:
2529:
2524:
2509:
2504:
2494:
2489:
2483:
2475:
2447:
2442:
2427:
2422:
2412:
2407:
2401:
2393:
2371:
2366:
2351:
2321:
2316:
2307:
2279:
2274:
2265:
2243:
2228:
2201:
2182:
2170:
2159:
2154:
2144:
2142:
2117:
2098:
2086:
2076:
2071:
2065:
2060:
2047:{\displaystyle SU(N_{f})_{L}^{2}U(1)_{R}}
2038:
2019:
2014:
2004:
1989:
1962:
1943:
1937:
1912:
1893:
1887:
1874:{\displaystyle SU(N_{f})_{L}^{2}U(1)_{B}}
1865:
1846:
1841:
1831:
1816:
1789:
1770:
1760:
1754:
1729:
1710:
1700:
1694:
1672:
1667:
1657:
1642:
1540:
1528:
1459:
1458:
1446:
1440:
1439:
1425:
1394:
1385:
1376:
1363:
1346:
1331:
1325:
1316:
1308:
1303:
1275:
1266:
1260:
1244:
1231:
1219:
1215:
1194:
1188:
1184:
1172:
1166:
1165:
1163:
1139:
1130:
1121:
1108:
1092:
1083:
1076:
1061:
1055:
1045:
1039:
1033:
1007:
998:
992:
976:
963:
951:
944:
934:
920:
909:
908:
906:
882:
873:
864:
851:
835:
826:
822:
806:
798:
793:
766:
744:
722:
712:
690:
680:
665:
643:
621:
599:
589:
567:
557:
542:
512:
499:
484:
459:
444:
395:
387:
378:. For a superconformal field theory, the
355:
341:
332:
319:
305:
303:
267:
254:
248:
176:Seiberg duality is an equivalence of the
109:Learn how and when to remove this message
2715:
1622:'t Hooft anomaly matching conditions
7:
2607:{\displaystyle U(1)_{B}^{2}U(1)_{R}}
1582:of the dual theories are identical.
47:adding citations to reliable sources
2985:Supersymmetric quantum field theory
1801:{\displaystyle N_{c}d^{(3)}(N_{f})}
1741:{\displaystyle N_{c}d^{(3)}(N_{f})}
14:
1681:{\displaystyle SU(N_{f})_{L}^{3}}
411:{\displaystyle D={\frac {3}{2}}R}
238:are positive integers satisfying
145:group flow they flow to the same
282:{\displaystyle N_{f}>N_{c}+1}
172:The statement of Seiberg duality
23:
2815:10.1016/j.nuclphysb.2009.01.028
524:{\displaystyle SU(N_{f}-N_{c})}
218:) and an N=1 chiral QCD with N
34:needs additional citations for
2595:
2588:
2571:
2564:
2363:
2356:
2240:
2233:
2207:
2194:
2189:
2183:
2123:
2110:
2105:
2099:
2035:
2028:
2011:
1997:
1974:{\displaystyle d^{(2)}(N_{f})}
1968:
1955:
1950:
1944:
1924:{\displaystyle d^{(2)}(N_{f})}
1918:
1905:
1900:
1894:
1862:
1855:
1838:
1824:
1795:
1782:
1777:
1771:
1735:
1722:
1717:
1711:
1664:
1650:
1552:{\displaystyle M\equiv Q^{c}Q}
1464:
1452:
1382:
1356:
1343:
1309:
1250:
1224:
1212:
1185:
1178:
1127:
1101:
1073:
1046:
982:
956:
941:
921:
914:
870:
844:
819:
799:
763:
756:
741:
734:
719:
705:
687:
673:
640:
633:
618:
611:
596:
582:
564:
550:
518:
492:
465:
452:
1:
2928:10.1088/1126-6708/2008/11/043
2875:10.1088/1126-6708/2000/08/052
1417:The dual theory contains the
2758:10.1016/0550-3213(94)00023-8
2380:{\displaystyle U(1)_{R}^{3}}
2336:{\displaystyle -N_{c}^{2}-1}
2294:{\displaystyle -N_{c}^{2}-1}
1597:Hanany–Witten brane cartoons
1574:Evidence for Seiberg duality
1337:
1200:
1067:
2964:Supersymmetric Field Theory
1616:anomaly matching conditions
1599:consisting of intersecting
1498:'t Hooft–Polyakov monopoles
535:global internal symmetries
380:anomalous scaling dimension
376:superconformal field theory
3016:
1510:dual superconducting model
160:with N=1 supersymmetry of
785:
471:{\displaystyle SU(N_{c})}
149:, and so are in the same
2252:{\displaystyle U(1)_{R}}
153:. It is an extension to
382:of a chiral superfield
137:relating two different
2990:Quantum chromodynamics
2656:
2632:
2608:
2545:
2463:
2381:
2337:
2295:
2253:
2214:
2130:
2048:
1975:
1925:
1875:
1802:
1742:
1682:
1591:It may be embedded in
1553:
1474:
1406:
1287:
1151:
1019:
894:
776:
653:
525:
472:
412:
365:
283:
162:Montonen–Olive duality
3000:Renormalization group
2681:quiver gauge theories
2657:
2633:
2609:
2546:
2464:
2382:
2338:
2296:
2254:
2215:
2131:
2049:
1976:
1926:
1876:
1803:
1743:
1683:
1554:
1500:. In particular, the
1475:
1407:
1288:
1152:
1020:
895:
777:
654:
526:
473:
413:
366:
284:
2643:
2619:
2558:
2474:
2392:
2350:
2306:
2264:
2227:
2141:
2059:
1988:
1936:
1886:
1815:
1753:
1693:
1641:
1527:
1424:
1302:
1162:
1032:
905:
792:
664:
541:
483:
443:
386:
302:
247:
123:quantum field theory
43:improve this article
2920:2008JHEP...11..043A
2867:2000JHEP...08..052K
2807:2009NuPhB.818..137D
2750:1995NuPhB.435..129S
2584:
2534:
2514:
2499:
2452:
2432:
2417:
2376:
2326:
2284:
2164:
2081:
2024:
1851:
1677:
1623:
786:chiral superfields
184:=1 theory with SU(N
139:supersymmetric QCDs
2655:{\displaystyle -2}
2652:
2631:{\displaystyle -2}
2628:
2604:
2570:
2541:
2520:
2500:
2485:
2459:
2438:
2418:
2403:
2377:
2362:
2333:
2312:
2291:
2270:
2249:
2210:
2150:
2126:
2067:
2044:
2010:
1971:
1921:
1871:
1837:
1798:
1738:
1678:
1663:
1621:
1549:
1496:) with nonabelian
1470:
1402:
1283:
1147:
1015:
890:
772:
649:
521:
468:
437:color gauge group
408:
361:
279:
151:universality class
2697:Matthew Strassler
2685:flavor symmetries
2665:
2664:
2515:
2433:
2176:
2092:
1568:global symmetries
1467:
1455:
1415:
1414:
1340:
1203:
1181:
1070:
917:
403:
349:
313:
204:chiral multiplets
129:, conjectured by
119:
118:
111:
93:
58:"Seiberg duality"
3007:
2995:Duality theories
2952:Nathan Seiberg,
2940:
2939:
2913:
2893:
2887:
2886:
2860:
2833:
2827:
2826:
2800:
2776:
2770:
2769:
2743:
2734:(1–2): 129–146.
2720:
2661:
2659:
2658:
2653:
2637:
2635:
2634:
2629:
2613:
2611:
2610:
2605:
2603:
2602:
2583:
2578:
2550:
2548:
2547:
2542:
2533:
2528:
2516:
2513:
2508:
2498:
2493:
2484:
2468:
2466:
2465:
2460:
2451:
2446:
2434:
2431:
2426:
2416:
2411:
2402:
2386:
2384:
2383:
2378:
2375:
2370:
2342:
2340:
2339:
2334:
2325:
2320:
2300:
2298:
2297:
2292:
2283:
2278:
2258:
2256:
2255:
2250:
2248:
2247:
2219:
2217:
2216:
2211:
2206:
2205:
2193:
2192:
2177:
2175:
2174:
2165:
2163:
2158:
2145:
2135:
2133:
2132:
2127:
2122:
2121:
2109:
2108:
2093:
2091:
2090:
2080:
2075:
2066:
2053:
2051:
2050:
2045:
2043:
2042:
2023:
2018:
2009:
2008:
1980:
1978:
1977:
1972:
1967:
1966:
1954:
1953:
1930:
1928:
1927:
1922:
1917:
1916:
1904:
1903:
1880:
1878:
1877:
1872:
1870:
1869:
1850:
1845:
1836:
1835:
1807:
1805:
1804:
1799:
1794:
1793:
1781:
1780:
1765:
1764:
1747:
1745:
1744:
1739:
1734:
1733:
1721:
1720:
1705:
1704:
1687:
1685:
1684:
1679:
1676:
1671:
1662:
1661:
1624:
1564:gauge symmetries
1558:
1556:
1555:
1550:
1545:
1544:
1508:phase as in the
1479:
1477:
1476:
1471:
1469:
1468:
1460:
1457:
1456:
1451:
1450:
1441:
1411:
1409:
1408:
1403:
1401:
1400:
1399:
1398:
1389:
1381:
1380:
1368:
1367:
1341:
1336:
1335:
1326:
1321:
1320:
1292:
1290:
1289:
1284:
1282:
1281:
1280:
1279:
1270:
1265:
1264:
1249:
1248:
1236:
1235:
1223:
1204:
1199:
1198:
1189:
1183:
1182:
1177:
1176:
1167:
1156:
1154:
1153:
1148:
1146:
1145:
1144:
1143:
1134:
1126:
1125:
1113:
1112:
1097:
1096:
1087:
1071:
1066:
1065:
1056:
1044:
1043:
1024:
1022:
1021:
1016:
1014:
1013:
1012:
1011:
1002:
997:
996:
981:
980:
968:
967:
955:
939:
938:
919:
918:
910:
899:
897:
896:
891:
889:
888:
887:
886:
877:
869:
868:
856:
855:
840:
839:
830:
811:
810:
781:
779:
778:
773:
771:
770:
749:
748:
727:
726:
717:
716:
695:
694:
685:
684:
658:
656:
655:
650:
648:
647:
626:
625:
604:
603:
594:
593:
572:
571:
562:
561:
530:
528:
527:
522:
517:
516:
504:
503:
477:
475:
474:
469:
464:
463:
424:
417:
415:
414:
409:
404:
396:
370:
368:
367:
362:
360:
359:
350:
342:
337:
336:
324:
323:
314:
306:
288:
286:
285:
280:
272:
271:
259:
258:
230:flavors, where N
114:
107:
103:
100:
94:
92:
51:
27:
19:
3015:
3014:
3010:
3009:
3008:
3006:
3005:
3004:
2970:
2969:
2949:
2947:Further reading
2944:
2943:
2895:
2894:
2890:
2841:Strassler, M.J.
2835:
2834:
2830:
2778:
2777:
2773:
2722:
2721:
2717:
2712:
2683:, in which the
2677:
2675:Generalizations
2641:
2640:
2617:
2616:
2594:
2556:
2555:
2472:
2471:
2390:
2389:
2348:
2347:
2304:
2303:
2262:
2261:
2239:
2225:
2224:
2197:
2178:
2166:
2146:
2139:
2138:
2113:
2094:
2082:
2057:
2056:
2034:
2000:
1986:
1985:
1958:
1939:
1934:
1933:
1908:
1889:
1884:
1883:
1861:
1827:
1813:
1812:
1785:
1766:
1756:
1751:
1750:
1725:
1706:
1696:
1691:
1690:
1653:
1639:
1638:
1612:Gerard 't Hooft
1576:
1536:
1525:
1524:
1504:is dual to the
1486:
1442:
1422:
1421:
1390:
1372:
1359:
1342:
1327:
1312:
1300:
1299:
1271:
1256:
1240:
1227:
1211:
1190:
1168:
1160:
1159:
1135:
1117:
1104:
1088:
1072:
1057:
1035:
1030:
1029:
1003:
988:
972:
959:
940:
930:
903:
902:
878:
860:
847:
831:
818:
802:
790:
789:
762:
740:
718:
708:
686:
676:
662:
661:
639:
617:
595:
585:
563:
553:
539:
538:
508:
495:
481:
480:
455:
441:
440:
384:
383:
351:
328:
315:
300:
299:
263:
250:
245:
244:
237:
233:
229:
225:
221:
212:antifundamental
209:
195:
187:
178:IR fixed points
174:
143:renormalization
133:in 1994, is an
127:Seiberg duality
115:
104:
98:
95:
52:
50:
40:
28:
17:
12:
11:
5:
3013:
3011:
3003:
3002:
2997:
2992:
2987:
2982:
2980:Gauge theories
2972:
2971:
2968:
2967:
2957:
2948:
2945:
2942:
2941:
2888:
2858:hep-th/0007191
2837:Klebanov, I.R.
2828:
2791:(3): 137–178.
2771:
2741:hep-th/9411149
2714:
2713:
2711:
2708:
2689:superpotential
2676:
2673:
2663:
2662:
2651:
2648:
2638:
2627:
2624:
2614:
2601:
2597:
2593:
2590:
2587:
2582:
2577:
2573:
2569:
2566:
2563:
2552:
2551:
2540:
2537:
2532:
2527:
2523:
2519:
2512:
2507:
2503:
2497:
2492:
2488:
2482:
2479:
2469:
2458:
2455:
2450:
2445:
2441:
2437:
2430:
2425:
2421:
2415:
2410:
2406:
2400:
2397:
2387:
2374:
2369:
2365:
2361:
2358:
2355:
2344:
2343:
2332:
2329:
2324:
2319:
2315:
2311:
2301:
2290:
2287:
2282:
2277:
2273:
2269:
2259:
2246:
2242:
2238:
2235:
2232:
2221:
2220:
2209:
2204:
2200:
2196:
2191:
2188:
2185:
2181:
2173:
2169:
2162:
2157:
2153:
2149:
2136:
2125:
2120:
2116:
2112:
2107:
2104:
2101:
2097:
2089:
2085:
2079:
2074:
2070:
2064:
2054:
2041:
2037:
2033:
2030:
2027:
2022:
2017:
2013:
2007:
2003:
1999:
1996:
1993:
1982:
1981:
1970:
1965:
1961:
1957:
1952:
1949:
1946:
1942:
1931:
1920:
1915:
1911:
1907:
1902:
1899:
1896:
1892:
1881:
1868:
1864:
1860:
1857:
1854:
1849:
1844:
1840:
1834:
1830:
1826:
1823:
1820:
1809:
1808:
1797:
1792:
1788:
1784:
1779:
1776:
1773:
1769:
1763:
1759:
1748:
1737:
1732:
1728:
1724:
1719:
1716:
1713:
1709:
1703:
1699:
1688:
1675:
1670:
1666:
1660:
1656:
1652:
1649:
1646:
1635:
1634:
1631:
1628:
1575:
1572:
1548:
1543:
1539:
1535:
1532:
1485:
1482:
1466:
1463:
1454:
1449:
1445:
1438:
1435:
1432:
1429:
1419:superpotential
1413:
1412:
1397:
1393:
1388:
1384:
1379:
1375:
1371:
1366:
1362:
1358:
1355:
1352:
1349:
1345:
1339:
1334:
1330:
1324:
1319:
1315:
1311:
1307:
1297:
1294:
1293:
1278:
1274:
1269:
1263:
1259:
1255:
1252:
1247:
1243:
1239:
1234:
1230:
1226:
1222:
1218:
1214:
1210:
1207:
1202:
1197:
1193:
1187:
1180:
1175:
1171:
1157:
1142:
1138:
1133:
1129:
1124:
1120:
1116:
1111:
1107:
1103:
1100:
1095:
1091:
1086:
1082:
1079:
1075:
1069:
1064:
1060:
1054:
1051:
1048:
1042:
1038:
1026:
1025:
1010:
1006:
1001:
995:
991:
987:
984:
979:
975:
971:
966:
962:
958:
954:
950:
947:
943:
937:
933:
929:
926:
923:
916:
913:
900:
885:
881:
876:
872:
867:
863:
859:
854:
850:
846:
843:
838:
834:
829:
825:
821:
817:
814:
809:
805:
801:
797:
787:
783:
782:
769:
765:
761:
758:
755:
752:
747:
743:
739:
736:
733:
730:
725:
721:
715:
711:
707:
704:
701:
698:
693:
689:
683:
679:
675:
672:
669:
659:
646:
642:
638:
635:
632:
629:
624:
620:
616:
613:
610:
607:
602:
598:
592:
588:
584:
581:
578:
575:
570:
566:
560:
556:
552:
549:
546:
536:
532:
531:
520:
515:
511:
507:
502:
498:
494:
491:
488:
478:
467:
462:
458:
454:
451:
448:
438:
434:
433:
430:
427:
407:
402:
399:
394:
391:
372:
371:
358:
354:
348:
345:
340:
335:
331:
327:
322:
318:
312:
309:
293:
292:
291:
290:
278:
275:
270:
266:
262:
257:
253:
235:
231:
227:
223:
219:
207:
193:
185:
173:
170:
158:gauge theories
147:IR fixed point
131:Nathan Seiberg
117:
116:
99:September 2014
31:
29:
22:
15:
13:
10:
9:
6:
4:
3:
2:
3012:
3001:
2998:
2996:
2993:
2991:
2988:
2986:
2983:
2981:
2978:
2977:
2975:
2965:
2961:
2958:
2955:
2951:
2950:
2946:
2937:
2933:
2929:
2925:
2921:
2917:
2912:
2907:
2903:
2899:
2892:
2889:
2884:
2880:
2876:
2872:
2868:
2864:
2859:
2854:
2850:
2846:
2842:
2838:
2832:
2829:
2824:
2820:
2816:
2812:
2808:
2804:
2799:
2794:
2790:
2786:
2785:Nucl. Phys. B
2782:
2775:
2772:
2767:
2763:
2759:
2755:
2751:
2747:
2742:
2737:
2733:
2729:
2728:Nucl. Phys. B
2725:
2719:
2716:
2709:
2707:
2705:
2700:
2698:
2694:
2693:Igor Klebanov
2690:
2686:
2682:
2674:
2672:
2670:
2649:
2646:
2639:
2625:
2622:
2615:
2599:
2591:
2585:
2580:
2575:
2567:
2561:
2554:
2553:
2538:
2535:
2530:
2525:
2521:
2517:
2510:
2505:
2501:
2495:
2490:
2486:
2480:
2477:
2470:
2456:
2453:
2448:
2443:
2439:
2435:
2428:
2423:
2419:
2413:
2408:
2404:
2398:
2395:
2388:
2372:
2367:
2359:
2353:
2346:
2345:
2330:
2327:
2322:
2317:
2313:
2309:
2302:
2288:
2285:
2280:
2275:
2271:
2267:
2260:
2244:
2236:
2230:
2223:
2222:
2202:
2198:
2186:
2179:
2171:
2167:
2160:
2155:
2151:
2147:
2137:
2118:
2114:
2102:
2095:
2087:
2083:
2077:
2072:
2068:
2062:
2055:
2039:
2031:
2025:
2020:
2015:
2005:
2001:
1994:
1991:
1984:
1983:
1963:
1959:
1947:
1940:
1932:
1913:
1909:
1897:
1890:
1882:
1866:
1858:
1852:
1847:
1842:
1832:
1828:
1821:
1818:
1811:
1810:
1790:
1786:
1774:
1767:
1761:
1757:
1749:
1730:
1726:
1714:
1707:
1701:
1697:
1689:
1673:
1668:
1658:
1654:
1647:
1644:
1637:
1636:
1632:
1629:
1626:
1625:
1619:
1617:
1613:
1608:
1606:
1602:
1598:
1594:
1593:string theory
1589:
1586:
1583:
1581:
1580:moduli spaces
1573:
1571:
1569:
1565:
1560:
1546:
1541:
1537:
1533:
1530:
1522:
1518:
1513:
1511:
1507:
1503:
1499:
1495:
1491:
1483:
1481:
1461:
1447:
1443:
1436:
1433:
1430:
1427:
1420:
1395:
1391:
1386:
1377:
1373:
1369:
1364:
1360:
1353:
1350:
1347:
1332:
1328:
1322:
1317:
1313:
1305:
1298:
1296:
1295:
1276:
1272:
1267:
1261:
1257:
1253:
1245:
1241:
1237:
1232:
1228:
1220:
1216:
1208:
1205:
1195:
1191:
1173:
1169:
1158:
1140:
1136:
1131:
1122:
1118:
1114:
1109:
1105:
1098:
1093:
1089:
1084:
1080:
1077:
1062:
1058:
1052:
1049:
1040:
1036:
1028:
1027:
1008:
1004:
999:
993:
989:
985:
977:
973:
969:
964:
960:
952:
948:
945:
935:
931:
927:
924:
911:
901:
883:
879:
874:
865:
861:
857:
852:
848:
841:
836:
832:
827:
823:
815:
812:
807:
803:
795:
788:
784:
767:
759:
753:
750:
745:
737:
731:
728:
723:
713:
709:
702:
699:
696:
691:
681:
677:
670:
667:
660:
644:
636:
630:
627:
622:
614:
608:
605:
600:
590:
586:
579:
576:
573:
568:
558:
554:
547:
544:
537:
534:
533:
513:
509:
505:
500:
496:
489:
486:
479:
460:
456:
449:
446:
439:
436:
435:
431:
428:
426:
425:
422:
419:
405:
400:
397:
392:
389:
381:
377:
356:
352:
346:
343:
338:
333:
329:
325:
320:
316:
310:
307:
298:
297:
296:
276:
273:
268:
264:
260:
255:
251:
243:
242:
241:
240:
239:
217:
213:
205:
202:
198:
191:
183:
179:
171:
169:
167:
163:
159:
156:
152:
148:
144:
140:
136:
132:
128:
124:
113:
110:
102:
91:
88:
84:
81:
77:
74:
70:
67:
63:
60: –
59:
55:
54:Find sources:
48:
44:
38:
37:
32:This article
30:
26:
21:
20:
2901:
2897:
2891:
2848:
2844:
2831:
2788:
2784:
2774:
2731:
2727:
2718:
2704:Chern–Simons
2701:
2678:
2669:Witten index
2666:
1633:dual theory
1609:
1590:
1587:
1584:
1577:
1561:
1514:
1487:
1416:
432:dual theory
420:
373:
294:
226:colors and N
181:
175:
126:
120:
105:
96:
86:
79:
72:
65:
53:
41:Please help
36:verification
33:
2779:Dolan, F.;
2724:Seiberg, N.
1506:confinement
1502:Higgs phase
216:bare masses
210:flavors of
201:fundamental
190:gauge group
2974:Categories
2960:David Tong
2904:(11): 43.
2781:Osborn, H.
2710:References
168:theories.
155:nonabelian
69:newspapers
2911:0807.4924
2851:(8): 52.
2798:0801.4947
2647:−
2623:−
2536:−
2478:−
2454:−
2396:−
2328:−
2310:−
2286:−
2268:−
2148:−
2063:−
1605:NS5-brane
1534:≡
1465:~
1453:~
1434:α
1370:−
1338:¯
1238:−
1201:¯
1179:~
1115:−
1078:−
1068:¯
970:−
946:−
915:~
858:−
751:×
729:×
697:×
628:×
606:×
574:×
506:−
188:) as the
135:S-duality
2936:14124024
2823:11829743
2766:18466754
1627:anomaly
1601:D-branes
2916:Bibcode
2883:2484915
2863:Bibcode
2803:Bibcode
2746:Bibcode
2706:terms.
1521:baryons
197:flavors
166:abelian
83:scholar
2934:
2881:
2821:
2764:
1517:mesons
1494:quarks
1490:gluons
180:in an
85:
78:
71:
64:
56:
2932:S2CID
2906:arXiv
2879:S2CID
2853:arXiv
2819:S2CID
2793:arXiv
2762:S2CID
2736:arXiv
1630:SQCD
429:SQCD
234:and N
206:and N
192:and N
90:JSTOR
76:books
2902:2008
2898:JHEP
2845:JHEP
2695:and
1595:via
1578:The
1562:The
1519:and
1515:The
339:<
326:<
261:>
62:news
2924:doi
2871:doi
2811:doi
2789:818
2754:doi
2732:435
1614:'s
199:of
121:In
45:by
2976::
2962:,
2930:.
2922:.
2914:.
2900:.
2877:.
2869:.
2861:.
2849:08
2847:.
2839:;
2817:.
2809:.
2801:.
2787:.
2760:.
2752:.
2744:.
2730:.
2699:.
1512:.
1480:.
222:-N
125:,
2966:.
2956:.
2938:.
2926::
2918::
2908::
2885:.
2873::
2865::
2855::
2825:.
2813::
2805::
2795::
2768:.
2756::
2748::
2738::
2650:2
2626:2
2600:R
2596:)
2592:1
2589:(
2586:U
2581:2
2576:B
2572:)
2568:1
2565:(
2562:U
2539:1
2531:2
2526:c
2522:N
2518:+
2511:2
2506:f
2502:N
2496:4
2491:c
2487:N
2481:2
2457:1
2449:2
2444:c
2440:N
2436:+
2429:2
2424:f
2420:N
2414:4
2409:c
2405:N
2399:2
2373:3
2368:R
2364:)
2360:1
2357:(
2354:U
2331:1
2323:2
2318:c
2314:N
2289:1
2281:2
2276:c
2272:N
2245:R
2241:)
2237:1
2234:(
2231:U
2208:)
2203:f
2199:N
2195:(
2190:)
2187:2
2184:(
2180:d
2172:f
2168:N
2161:2
2156:c
2152:N
2124:)
2119:f
2115:N
2111:(
2106:)
2103:2
2100:(
2096:d
2088:f
2084:N
2078:2
2073:c
2069:N
2040:R
2036:)
2032:1
2029:(
2026:U
2021:2
2016:L
2012:)
2006:f
2002:N
1998:(
1995:U
1992:S
1969:)
1964:f
1960:N
1956:(
1951:)
1948:2
1945:(
1941:d
1919:)
1914:f
1910:N
1906:(
1901:)
1898:2
1895:(
1891:d
1867:B
1863:)
1859:1
1856:(
1853:U
1848:2
1843:L
1839:)
1833:f
1829:N
1825:(
1822:U
1819:S
1796:)
1791:f
1787:N
1783:(
1778:)
1775:3
1772:(
1768:d
1762:c
1758:N
1736:)
1731:f
1727:N
1723:(
1718:)
1715:3
1712:(
1708:d
1702:c
1698:N
1674:3
1669:L
1665:)
1659:f
1655:N
1651:(
1648:U
1645:S
1547:Q
1542:c
1538:Q
1531:M
1462:Q
1448:c
1444:Q
1437:M
1431:=
1428:W
1396:f
1392:N
1387:/
1383:)
1378:c
1374:N
1365:f
1361:N
1357:(
1354:2
1351:,
1348:0
1344:)
1333:f
1329:N
1323:,
1318:f
1314:N
1310:(
1306:M
1277:f
1273:N
1268:/
1262:c
1258:N
1254:,
1251:)
1246:c
1242:N
1233:f
1229:N
1225:(
1221:/
1217:1
1213:)
1209:1
1206:,
1196:f
1192:N
1186:(
1174:c
1170:Q
1141:f
1137:N
1132:/
1128:)
1123:c
1119:N
1110:f
1106:N
1102:(
1099:,
1094:c
1090:N
1085:/
1081:1
1074:)
1063:f
1059:N
1053:,
1050:1
1047:(
1041:c
1037:Q
1009:f
1005:N
1000:/
994:c
990:N
986:,
983:)
978:c
974:N
965:f
961:N
957:(
953:/
949:1
942:)
936:f
932:N
928:,
925:1
922:(
912:Q
884:f
880:N
875:/
871:)
866:c
862:N
853:f
849:N
845:(
842:,
837:c
833:N
828:/
824:1
820:)
816:1
813:,
808:f
804:N
800:(
796:Q
768:R
764:)
760:1
757:(
754:U
746:B
742:)
738:1
735:(
732:U
724:R
720:)
714:f
710:N
706:(
703:U
700:S
692:L
688:)
682:f
678:N
674:(
671:U
668:S
645:R
641:)
637:1
634:(
631:U
623:B
619:)
615:1
612:(
609:U
601:R
597:)
591:f
587:N
583:(
580:U
577:S
569:L
565:)
559:f
555:N
551:(
548:U
545:S
519:)
514:c
510:N
501:f
497:N
493:(
490:U
487:S
466:)
461:c
457:N
453:(
450:U
447:S
406:R
401:2
398:3
393:=
390:D
357:f
353:N
347:3
344:2
334:c
330:N
321:f
317:N
311:3
308:1
289:.
277:1
274:+
269:c
265:N
256:f
252:N
236:f
232:c
228:f
224:c
220:f
208:f
194:f
186:c
182:N
112:)
106:(
101:)
97:(
87:·
80:·
73:·
66:·
39:.
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
