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

Abstract

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.

Superconformal index, BPS monodromy and chiral algebras

“…For example for SU (2) with N f = 4 we expect h min = −1. The fact that h min should be negative for N < 0 implies that (5c 4d − 4a 4d ) > 0 which is consistent with the unitarity bound [22]. Moreover if we have a rational 2d chiral algebra, it is expected that this combination is rational.…”

“…Below we shall show that this prediction is correct, and identify the lattice Λ n and the precise two variable specialization. 22 We thank Ole Warnaar for communicating his proof to us. 23 Also for n = 1, taking into account that the quoted value of k refers to the diagonal SU(2) subgroup.…”

“…Using this and the r-charges for the Coulomb branch of the (G, G ) models which are known, one can also deduce a 4d for all (G, G ) AD theories from the relation [22] 4(2a…”

“…(7.59)), originally motivated by the Sugawara saturation and its implications for the monodromy M(q), has recently been proved by O. Warnaar [61]. 22 …”

“…The 4d central charge (a, c) of the generalized ArgyresDouglas theory of type (A k−1 , A n−1 ) is given as [22,67,68] …”