Holographic Coulomb branch solitons, quasinormal modes, and black holes

Four-dimensional N=4 supersymmetric Yang-Mills theory, at a point on the Coulomb branch where SU(N) gauge symmetry is spontaneously broken to SU(N − 1) × U(1), admits BPS solitons describing a spherical shell of electric and/or magnetic charges enclosing a region of unbroken gauge symmetry. These solitons have been proposed as gauge theory models for certain features of asymptotically flat extremal black holes. In the ’t Hooft large N limit with large ’t Hooft coupling, these solitons are holographically dual to certain probe D3-branes in the AdS5 ×S5 solution of type IIB supergravity. By studying linearised perturbations of these D3-branes, we show that the solitons support quasinormal modes with a spectrum of frequencies sharing both qualitative and quantitative features with asymptotically flat extremal black holes

Integrable deformations of AdS/CFT

In this paper we study in detail the deformations introduced in [1] of the integrable structures of the AdS$_{2,3}$ integrable models. We do this by embedding the corresponding scattering matrices into the most general solutions of the Yang-Baxter equation. We show that there are several non-trivial embeddings and corresponding deformations. We work out crossing symmetry for these models and study their symmetry algebras and representations. In particular, we identify a new elliptic deformation of the $\rm AdS_3 \times S^3 \times M^4$ string sigma model.Comment: v2: We corrected typos and added some references; v3: corrected crossing for AdS2 deformatio

Holographic entanglement entropy of the Coulomb branch

We compute entanglement entropy (EE) of a spherical region in (3 + 1)- dimensional N = 4 supersymmetric SU(N) Yang-Mills theory in states described holographically by probe D3-branes in AdS5 × S5. We do so by generalising methods for computing EE from a probe brane action without having to determine the probe’s back- reaction. On the Coulomb branch with SU(N) broken to SU(N − 1) × U(1), we find the EE monotonically decreases as the sphere’s radius increases, consistent with the a-theorem. The EE of a symmetric-representation Wilson line screened in SU(N − 1) also monotonically decreases, although no known physical principle requires this. A spherical soliton separating SU(N) inside from SU(N − 1) × U(1) outside had been proposed to model an extremal black hole. However, we find the EE of a sphere at the soliton’s radius does not scale with the surface area. For both the screened Wilson line and soliton, the EE at large radius is described by a position-dependent W-boson mass as a short-distance cutoff. Our holographic results for EE and one-point functions of the Lagrangian and stress-energy tensor show that at large distance the soliton looks like a Wilson line in a direct product of fundamental representations

Free Fermions, vertex Hamiltonians, and lower-dimensional AdS/CFT

In this paper we first demonstrate explicitly that the new models of integrable nearest-neighbour Hamiltonians recently introduced in PRL 125 (2020) 031604 satisfy the so-called free fermion condition. This both implies that all these models are amenable to reformulations as free fermion theories, and establishes the universality of this condition. We explicitly recast the transfer matrix in free fermion form for arbitrary number of sites in the 6-vertex sector, and on two sites in the 8-vertex sector, using a Bogoliubov transformation. We then put this observation to use in lower-dimensional instances of AdS/CFT integrable R-matrices, specifically pure Ramond-Ramond massless and massive AdS_3, mixed-flux relativistic AdS_3 and massless AdS_2. We also attack the class of models akin to AdS_5 with our free fermion machinery. In all cases we use the free fermion realisation to greatly simplify and reinterpret a wealth of known results, and to provide a very suggestive reformulation of the spectral problem in all these situations.Comment: 51 pages, no figures; v2: typos fixed and comments added; v3: 54 pages, typos and errors fixed, added comments, homogenised notation, added appendi

Ground state energy of twisted AdS 3 × S 3 × T 4 superstring and the TBA

Abstract We use the lightcone AdS 3 × S 3 × T 4 superstring sigma model with fermions and bosons subject to twisted boundary conditions to find the ground state energy in the semi-classical approximation where effective string tension h and the light-cone momentum L are sent to infinity in such a way that J $$\mathcal{J}$$ ≡ L/h is kept fixed. We then analyse the ground state energy of the model by means of the mirror TBA equations for the AdS 3 × S 3 × T 4 superstring in the pure RR background. The calculation is performed for small twist μ with L and h fixed, for large L with μ and h fixed, and for small h with μ and L fixed. In these limits the contribution of the gapless worldsheet modes coming from the T 4 bosons and fermions can be computed exactly, and is shown to be proportional to hL/(4L 2 – 1). Comparison with the semi-classical result shows that the TBA equations involve only one Y 0-function for massless excitations but not two as was conjectured before. Some of the results obtained are generalised to the mixed-flux AdS 3 × S 3 × T 4 superstring