Low energy dynamics from deformed conformal symmetry in quantum 4D N = 2 SCFTs

TL;DR

This paper calculates one-loop deformations of conformal symmetry in various N=2 superconformal Yang-Mills theories, revealing how quantum corrections affect the symmetry algebra and constraining the effective action on Coulomb branches.

Contribution

It provides explicit one-loop deformations of conformal symmetry for several N=2 theories, including N=4 SYM and quiver models, and determines higher-loop corrections needed for algebra closure.

Findings

One-loop deformation realizes the conformal algebra in N=4 SYM.

Higher-loop corrections are necessary for other models to close the algebra.

Quantum corrections impose restrictions on the effective action.

Abstract

We determine the one-loop deformation of the conformal symmetry of a general N}=2 superconformally invariant Yang-Mills theory. The deformation is computed for several explicit examples which have a realization as world-volume theories on a stack of D3 branes. These include (i) N=4 SYM with gauge groups SU(N), USp(2N) and SO(N); (ii) USp(2N) gauge theory with one hypermultiplet in the traceless antisymmetric representation and four hypermultiplets in the fundamental; (iii) quiver gauge theory with gauge group SU(N)xSU(N) and two hypermultiplets in the bifundamental representations (N,\bar N) and (bar N,N). The existence of quantum corrections to the conformal transformations imposes restrictions on the effective action which we study on a subset of the Coulomb branch corresponding to the separation of one brane from the stack. In the N=4 case, the one-loop corrected transformations provide a realization of the conformal algebra; this deformation is shown to be one-loop exact. For the other two models, higher-loop corrections are necessary to close the algebra. Requiring closure, we infer the two-loop conformal deformation.