Fermionic and bosonic mass deformations of N=4 SYM and their bulk supergravity dual

TL;DR

This paper explores the holographic duals of fermionic mass deformations in N=4 SYM, clarifying how bulk supergravity modes relate to fermion and boson mass matrices and resolving discrepancies about their stringy nature.

Contribution

It demonstrates that fermion masses fully determine the trace of the boson mass matrix and clarifies the supergravity modes corresponding to mass deformations, resolving previous tensions.

Findings

Fermion masses determine the trace of the boson mass matrix.

Non-normalizable modes correspond to traceless components of the boson mass matrix.

Asymptotically-AdS flows describe theories with equal sums of bosonic and fermionic mass squares.

Abstract

We examine the AdS-CFT dual of arbitrary (non)supersymmetric fermionic mass deformations of N=4 SYM, and investigate how the backreaction of the RR and NS-NS two-form potentials dual to the fermion masses contribute to Coulomb-branch potential of D3 branes, which we interpret as the bulk boson mass matrix. Using representation-theory and supergravity arguments we show that the fermion masses completely determine the trace of this matrix, and that on the other hand its traceless components have to be turned on as non-normalizable modes. Our result resolves the tension between the belief that the AdS bulk dual of the trace of the boson mass matrix (which is not a chiral operator) is a stringy excitation with dimension of order $(g_s N)^{1/4}$ and the existence of non-stringy supergravity flows describing theories where this trace is nonzero, by showing that the stringy mode does not parameterize the sum of the squares of the boson masses but rather its departure from the trace of the square of the fermion mass matrix. Hence, asymptotically-AdS flows can only describe holographically theories where the sums of the squares of the bosonic and fermionic masses are equal, which is consistent with the weakly-coupled result that only such theories can have a conformal UV fixed point.