Supersymmetric holomorphic masses in AdS/CFT with flavour

A bstract 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 $$ \left(z,\overline{z}\right) $$ z z ¯ and defining the D7-branes’ worldvolume scalars as $$ \left(y,\overline{y}\right) $$ y y ¯ , we prove that any holomorphic function y ( z ) or antiholomorphic function $$ y\left(\overline{z}\right) $$ y z ¯ is a BPS solution of the D7-branes’ equations of motion preserving $$ \mathcal{N} $$ 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 $$ \mathcal{N} $$ 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 $$ \mathcal{N} $$ 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, $$ m\left(\overline{z}\right) $$ m z ¯ . We provide field theory proofs, valid for any N c , N f , and ’t Hooft coupling, that such m preserve $$ \mathcal{N} $$ 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 ).