A quantum check of AdS/dCFT

Abstract

We build the framework for performing loop computations in the defect version of N = 4 super Yang-Mills theory which is dual to the probe D5-D3 brane system with background gauge-field flux. In this dCFT, a codimension-one defect separates two regions of space-time with different ranks of the gauge group and three of the scalar fields acquire non-vanishing and space-time-dependent vacuum expectation values. The latter leads to a highly non-trivial mass mixing problem between different colour and flavour components, which we solve using fuzzy-sphere coordinates. Furthermore, the resulting space-time dependence of the theory's Minkowski space propagators is handled by reformulating these as propagators in an effective AdS 4 . Subsequently, we initiate the computation of quantum corrections. The one-loop correction to the one-point function of any local gauge-invariant scalar operator is shown to receive contributions from only two Feynman diagrams. We regulate these diagrams using dimensional reduction, finding that one of the two diagrams vanishes, and discuss the procedure for calculating the one-point function of a generic operator from the SU(2) subsector. Finally, we explicitly evaluate the one-loop correction to the one-point function of the BPS vacuum state, finding perfect agreement with an earlier string-theory prediction. This constitutes a highly non-trivial test of the gauge-gravity duality in a situation where both supersymmetry and conformal symmetry are partially broken.

Spin chain overlaps and the twisted Yangian

“…The dCFT versions of N = 4 SYM theory with non-vanishing vevs and their dual string theory configurations. The discussion of the integrability properties of the corresponding matrix product states can be found in [13,14] and the closed expression for the overlap formula for the D3-D5 case appears in [9][10][11]13] for tree level and in [26] for one-loop, see also [27,28].…”

A quantum framework for AdS/dCFT through fuzzy spherical harmonics on S4

“…Inserting the expansion into the action of N = 4 SYM theory generates (spacetimedependent) mass terms for some of the fields, as well as novel cubic and quartic interaction terms. This has been worked out in detail in [24][25][26]. Upon insertion of the expansion (2.3), the kinetic terms of the action remain canonical, while the mass terms acquire a non-trivial mixing between different fields.…”

“…The first one involves only bosonic terms, and following [25] we call it easy because the mixing only involves color degrees of freedom,…”

“…The string theory configurations dual to the dCFT versions of N = 4 SYM theory with non-vanishing vevs. The discussion of the integrability properties of the corresponding boundary states can be found in [19,20] and the test of the match between gauge theory and string theory referred to in the first two columns can be found in [24][25][26].…”

“…We start by describing the diagonalization of the mass matrix in Section 2 and explicitly give the complete spectrum of quantum excitations including their multiplicities. The propagators of the fields which diagonalize the mass matrix are found following the procedure of [25], and due to the spacetime-dependence of the vevs, become propagators in an auxiliary AdS 4 space. For concrete perturbative calculations, it is convenient to have the contraction rules and propagators formulated in terms of the original fields of N = 4 SYM theory and the complete set of these are presented in Section 3.…”