TY - JOUR

T1 - Central charges of N = 2 superconformal field theories in four dimensions

AU - Shapere, Alfred D.

AU - Tachikawa, Yuji

PY - 2008/9/1

Y1 - 2008/9/1

N2 - We present a general method for computing the central charges a and c of N = 2 superconformal field theories corresponding to singular points in the moduli space of N = 2 gauge theories. Our method relates a and c to the U(1) R anomalies of the topologically twisted gauge theory. We evaluate these anomalies by studying the holomorphic dependence of the path integral measure on the moduli. We calculate a and c for superconformal points in a variety of gauge theories, including N = 4 SU(N), N = 2 pure SU(N) Yang-Mills, and USp(2N) with 1 massless antisymmetric and 4 massive fundamental hypermultiplets. In the latter case, we reproduce the conformal and flavor central charges previously calculated using the gravity duals of these gauge theories. For any SCFT in the class under consideration, we derive a previously conjectured expression for 2a-c in terms of the sum of the dimensions of operators parameterizing the Coulomb branch. Finally, we prove that the ratio a/c is bounded above by 5/4 and below by 1/2.

AB - We present a general method for computing the central charges a and c of N = 2 superconformal field theories corresponding to singular points in the moduli space of N = 2 gauge theories. Our method relates a and c to the U(1) R anomalies of the topologically twisted gauge theory. We evaluate these anomalies by studying the holomorphic dependence of the path integral measure on the moduli. We calculate a and c for superconformal points in a variety of gauge theories, including N = 4 SU(N), N = 2 pure SU(N) Yang-Mills, and USp(2N) with 1 massless antisymmetric and 4 massive fundamental hypermultiplets. In the latter case, we reproduce the conformal and flavor central charges previously calculated using the gravity duals of these gauge theories. For any SCFT in the class under consideration, we derive a previously conjectured expression for 2a-c in terms of the sum of the dimensions of operators parameterizing the Coulomb branch. Finally, we prove that the ratio a/c is bounded above by 5/4 and below by 1/2.

KW - Extended supersymmetry

KW - Supersymmetric gauge theory

KW - Supersymmetry and duality

KW - Topological field theories

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U2 - 10.1088/1126-6708/2008/09/109

DO - 10.1088/1126-6708/2008/09/109

M3 - Article

AN - SCOPUS:58149306152

SN - 1126-6708

VL - 2008

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

IS - 9

M1 - 109

ER -