Holographic RG flows for four-dimensional $$ \mathcal{N}=2 $$ SCFTs

Abstract

We study holographic renormalization group flows from four-dimensional N = 2 SCFTs to either N = 2 or N = 1 SCFTs. Our approach is based on the framework of five-dimensional half-maximal supergravity with general gauging, which we use to study domain wall solutions interpolating between different supersymmetric AdS 5 vacua. We show that a holographic RG flow connecting two N = 2 SCFTs is only possible if the flavor symmetry of the UV theory admits an SO(3) subgroup. In this case the ratio of the IR and UV central charges satisfies a universal relation which we also establish in field theory. In addition we provide several general examples of holographic flows from N = 2 to N = 1 SCFTs and relate the ratio of the UV and IR central charges to the conformal dimension of the operator triggering the flow. Instrumental to our analysis is a derivation of the general conditions for AdS vacua preserving eight supercharges as well as for domain wall solutions preserving eight Poincaré supercharges in half-maximal supergravity.

Holographic RG flows in $$N=4$$ N = 4 SCFTs from half-maximal gauged supergravity

“…The results found here is also in line with [18]. In particular, scalars in the gravity multiplet are dual to relevant operators at all critical points.…”

“…Another direction is to find interpretations of the solutions given here in the dual N = 4 CSM theories with different flavor symmetries similar to the recent study in [18] for AdS 5 /CFT 4 correspondence. The results found here is also in line with [18].…”

“…In this work, we will consider semisimple gauging of N = 4 supergravity similar to the study in other dimensions. Although some general properties of Ad S 4 vacua and RG flows have been pointed out recently in [18], to the best of our knowledge, a detailed analysis and explicit RG flow solutions in N = 4 gauged supergravity have not previously appeared.…”

Consistent KK truncations for M5-branes wrapped on Riemann surfaces

“…We conclude this subsection by proving that there are no further maximally supersymmetric AdS 5 vacua. In fact, given the gauge group is SO(2) × SE(3), the results of [10,25] imply that for l = −1 the above vacuum is necessarily unique. For l = 0 and l = +1, we need to analyse the conditions for maximal supersymmetry as presented in [10].…”

“…In fact, given the gauge group is SO(2) × SE(3), the results of [10,25] imply that for l = −1 the above vacuum is necessarily unique. For l = 0 and l = +1, we need to analyse the conditions for maximal supersymmetry as presented in [10]. Taking into account that [10] worked in a basis in which η was diagonal we first define…”