Generalizations of the AdS/CFT correspondence

TL;DR

The paper develops and analyzes generalizations of the AdS/CFT correspondence by introducing probe branes to build defect conformal field theories and QCD-like, flavoured gauge theories, enabling holographic studies of fundamental matter, chiral symmetry breaking, and meson spectra. It advances the holographic dictionary for dCFTs, demonstrates nontrivial flavor dynamics and phase transitions in non-supersymmetric backgrounds, and provides a comprehensive deconstruction program that connects defect CFTs to intersecting M5-branes and, more boldly, to M-theory on toroidal and orbifold backgrounds. Through explicit calculations of spectra and correlators, the work shows how holography can capture key nonperturbative phenomena in strongly coupled gauge theories and outlines a field-theoretic pathway to higher-dimensional theories via deconstruction. Overall, the results contribute to understanding flavor in holography, defect dynamics, and the Quest to realize M-theory data from four-dimensional gauge theories, with potential implications for modeling QCD-like dynamics and quantum gravity embeddings.

Abstract

We consider generalizations of the AdS/CFT correspondence in which probe branes are embedded in gravity backgrounds dual to either conformal or confining gauge theories. These correspond to defect conformal field theories (dCFT) or QCD-like theories with fundamental matter, respectively. Computing the quark condensate and the meson spectrum for a non-supersymmetric QCD-like theory from supergravity, we find spontaneous U(1) chiral symmetry breaking as well as the associated Goldstone boson. For another example at finite temperature, we observe a phase transition corresponding to a geometrical transition of the brane embedding. Moreover, starting from the dCFT we discuss the deconstruction of intersecting M5-branes. The resulting theory corresponds to two six-dimensional (2,0) superconformal field theories which we show to have tensionless strings on their four-dimensional intersection. Finally, we comment on the deconstruction of M-theory from a non-supersymmetric quiver gauge theory.

Figures (36)

• Figure 1.1: Standard AdS/CFT: The left figure shows the description of a stack of D3-branes in terms of open strings (Yang-Mills description), the right figure in terms of closed strings (supergravity description).
• Figure 1.2: Interaction of bulk gauge bosons and defect quarks.
• Figure 1.3: Holography of the D3-D5 brane intersection.
• Figure 1.4: Theory space (quiver diagram) for parallel D3-branes at a $\mathbb{C}^2/\mathbb{Z}_k$ orbifold. Each node corresponds to an ${\cal N} =2$ vector multiplet, while double lines between neighboring nodes correspond to an ${\cal N}=2$ hypermultiplet.
• Figure 2.1: AdS/CFT duality for an defect CFT. The duality acts twice. Once for the IIB supergravity on $AdS_5 \times S^5$, and once for DBI theory on $AdS_{k+2} \times S^k$.