Supersymmetric Holomorphic Masses in AdS/CFT with Flavour

TL;DR

This paper demonstrates that holomorphic or antiholomorphic mass functions in a holographic D3/D7-brane setup preserve specific supersymmetries and correspond to defect theories with zero energy and mass expectation values.

Contribution

It proves the supersymmetry-preserving nature of holomorphic mass functions in the AdS/CFT context and explores their dual field theory implications.

Findings

Holomorphic mass functions preserve N=(4,0) or (0,4) SUSY.

Mass functions with zeros correspond to superconformal defects.

The dual field theory exhibits zero energy and zero mass operator expectation.

Abstract

In type IIB supergravity (SUGRA), in the extremal background of a number N_c of D3-branes we consider a number N_f of probe D7-branes extended along all four D3-brane directions, (x_0,x_1,x_2,x_3). Using (x_2,x_3) to define complex coordinates (z,\bar{z}) and defining the D7-branes' worldvolume scalars as (y,\bar{y}), we prove that any holomorphic function y(z) or antiholomorphic function y(\bar{z}) is a BPS solution of the D7-branes' equations of motion preserving N=(4,0) or (0,4) supersymmetry (SUSY) along (x_0,x_1), respectively. In the near-horizon geometry, five-dimensional Anti-de Sitter (AdS) spacetime times a five-sphere, the AdS/Conformal Field Theory correspondence states that type IIB SUGRA is holographically dual to four-dimensional N=4 supersymmetric SU(N_c) Yang-Mills theory at large N_c and large 't Hooft coupling, and the N_f D7-branes are dual to N_f N=2 hypermultiplets in the fundamental representation, i.e. flavour fields. Our D7-brane solutions are dual to a position-dependent hypermultiplet mass m that is holomorphic, m(z), or antiholomorphic, m(\bar{z}). We provide field theory proofs, valid for any N_c, N_f, and 't Hooft coupling, that such m preserve N=(4,0) or (0,4) SUSY along (x_0,x_1). We also perform holographic calculations with probe D7-branes to show that the theory with such m has zero energy and zero expectation value of the mass operator, and that a zero of m is dual to a superconformal defect described by chiral fermions along (x_0,x_1).