Abstract
We examine the AdS-CFT dual of arbitrary (non)supersymmetric fermionic mass deformations of $$ \mathcal{N} $$ = 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.
Highlights
Fermionic massesThe most general non-supersymmetric fermionic mass deformation of N = 4 SYM is given by the operator:
Term was guessed by using supersymmetry to complete the squares in the polarization potential
Our main goal is to study the non-supersymmetric version of the Polchinski-Strassler story, and in particular to spell out a method to determine completely the D3-brane Coulomb branch potential for the N = 4 SYM theory deformed with a generic supersymmetry-breaking combination of fermion and boson masses
Summary
The most general non-supersymmetric fermionic mass deformation of N = 4 SYM is given by the operator:. The mass matrix M is in the 10 of SU(4), which is the symmetric part of 4 Ă 4:. In the language of N = 1, one distinguishes a U (1)R â SU (4)R that singles out the gaugino within the 4 fermions, or in other words the SU (4) R-symmetry group is broken as: SU (4)R â SU (3) Ă U (1)R (2.3). Corresponding to the splitting of the fundamental index 4 = 3 + 1 (i = {I, 4}). In this breaking, the fermionic mass matrix in the 10 decomposes as 10 = 6 + 3 + 1. MIJ m I m TI mwhere mIJ , m I and mare respectively in the 6, 3 and 1
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