Central charges of 𝒩 = 2 superconformal field theories in four dimensions
By A. Shapere, Yuji Tachikawa. Journal of High Energy Physics, 2008
242 citations recorded by the source corpus.
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.
Subfields: Nuclear and High Energy Physics
View Paper: https://www.semanticscholar.org/paper/0cc0ace291d7b43a83d9f25c15ce25cd95358b6f
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Citations in the corpus
- Geometric constraints on the space of N=2 SCFTs I: physical constraints on relevant deformations (2015, methodology): “But it is pointed out in [16] that the Shapere-Tachikawa calculus does not work for those theories obtained by discretely gauging a symmetry which acts non-trivially on the CB.”
- 4d Index to 3d Index and 2d TQFT (2011, background): “By comparing the definitions of the indices (compare (7)-(8) with (22)-(23), see also [20]) we obtain”
- Schur indices, BPS particles, and Argyres-Douglas theories (2015, methodology): “For the A2n+1 Argyres-Douglas theory, the 4d central charge is c4d = 3n2+5n+1 6(n+2) [30, 32, 48,49].”
- Quantum vortex strings: A review (2008, unknown): “In contrast, the central charges of the 4d theory was recently computed [77] and, as N → ∞, scale as a4d ∼ c4d ∼ O(N), reflecting the growing number of massless modes present in the 4d SCFT.”
- General Argyres-Douglas theory (2012, methodology): “By using the topological gauge theory, the author of [20] found the following formula:”
- N=1 Deformations and RG Flows of N=2 SCFTs (2016, methodology): “In this paper, we considered the N = 1 deformation of N = 2 SCFTs.”
- AdS7/CFT6, Gauss-Bonnet gravity, and viscosity bound (2009, background): “(More stringent bounds exist for N = 2 superconformal four dimensional field theories [7].”
- Top down approach to 6D SCFTs (2018, background): “This is a theory with no known Lagrangian description, though many properties of this theory such as its Seiberg-Witten curve, its Gaiotto curve [9], and its anomalies [181, 182] are known.”