Mapping out the internal space in AdS/BCFT with Wilson loops

Abstract

We study Wilson loops in string theory realizations of AdS/BCFT and wedge holography. The field theories are based on 3d N = 4 long quiver gauge theories engineered by D3, D5 and NS5 branes, and on BCFTs involving 4d N = 4 SYM coupled to such 3d theories. The holographic duals have geometry AdS 4 × S 2 × S 2 warped over a strip. We identify the holographic representation of antisymmetric Wilson loops associated with individual 3d gauge nodes in terms of probe D5-branes. The expectation values obtained holographically are matched to supersymmetric localization computations. Our results yield an identification of regions in the internal space with individual 3d gauge nodes. Connecting to bottom-up braneworld models, this gives a concrete notion of which parts of the 10d solutions correspond to the end-of-the-world brane and which to the remaining bulk. We also construct supersymmetric Janus on the brane embeddings in AdS 5 ×S 5 , which describe surface defects with boundaries and interfaces in N = 4 SYM.

Double holography in string theory

“…A concrete connection between regions in the 10d geometry and 3d/4d degrees of freedom was made in [31], by studying 1 2 -BPS Wilson loops in antisymmetric representations of individual 3d gauge nodes (and their mirror-dual vortex loops), identifying their holographic representation as probe D5 (and NS5 ) branes in the 10d solutions, and matching the expectation values to supersymmetric localization calculations. In this way, slices of the strip Σ can be linked to individual 3d gauge nodes.…”

“…To some extent one can still identify points on Σ between the two solutions, by characterizing them in terms of CFT data. We will illustrate this for Wilson loops, based on the results of [31]. We define a coordinate system on the brane diagram and discuss how it can be imported onto the strip Σ.…”

“…The D5 can be characterized by a horizontal coordinate in the brane diagram, specifying between which pair of NS5-branes the D5 is inserted, and a vertical coordinate specifying where along the corresponding D3-brane stack the D5 is inserted. In the supergravity solutions the Wilson loops are realized by probe D5 -branes wrapping AdS 2 in AdS 4 , a curve in Σ, the entire sphere S 2 1 , and an S 1 in S 2 2 [31]. The curve in Σ wrapped by the D5 corresponds to the gauge node which the Wilson loop is associated with, and how far the D5 extends along this curve encodes the rank of the representation.…”

“…One could consider more general limits where g ∼ 1/N β 5 with β > 0, but we will not discuss that here. In gauge theory terms the number of 3d gauge nodes is large and fixed in the limit (31) while the ranks and flavor numbers scale. In the BCFT dual (8) with the rescaling (22), h 1 is of order N D5 and h 2 of order N NS5 .…”

Brane Dynamics of Holographic BCFTs

“…For example, this includes condensed matter and field theoretic aspects of chaotic BCFTs [46][47][48][49][50][51][52][53][54][55][56][57], studies of boundary renormalization group flow and boundary entropy, [58][59][60][61], holographic calculations of the computational complexity [62][63][64][65][66][67][68][69] and cosmological models [70][71][72][73][74]. String theory embeddings have been studied in [75][76][77][78][79][80][81][82][83]. Moreover, the AdS/BCFT correspondence was generalized in [84,85] to construct gravity duals of higher codimension holography.…”