Conformal quantum mechanics & the integrable spinning Fishnet

In this paper we consider systems of quantum particles in the 4d Euclidean space which enjoy conformal symmetry. The algebraic relations for conformal-invariant combinations of positions and momenta are used to construct a solution of the Yang-Baxter equation in the unitary irreducibile representations of the principal series ∆ = 2 + iν for any left/right spins ℓ,$$ \dot{\ell} $$ ℓ ̇ of the particles. Such relations are interpreted in the language of Feynman diagrams as integral star-triangle identites between propagators of a conformal field theory. We prove the quantum integrability of a spin chain whose k-th site hosts a particle in the representation (∆k, ℓk,$$ \dot{\ell} $$ ℓ ̇ k) of the conformal group, realizing a spinning and inhomogeneous version of the quantum magnet used to describe the spectrum of the bi-scalar Fishnet theories [1]. For the special choice of particles in the scalar (1, 0, 0) and fermionic (3/2, 1, 0) representation the transfer matrices of the model are Bethe-Salpeter kernels for the double-scaling limit of specific two-point correlators in the γ-deformed $$ \mathcal{N} $$ N = 4 and $$ \mathcal{N} $$ N = 2 supersymmetric theories.

Horizon acoustics of the GHS black hole and the spectrum of AdS2

We uncover a novel structure in Einstein-Maxwell-dilaton gravity: an AdS2 × S2 solution in string frame, which can be obtained by a near-horizon limit of the extreme GHS black hole with dilaton coupling λ ≠ 1. Unlike the Bertotti-Robinson spacetime, our solution has independent length scales for the AdS2 and S2, with ratio controlled by λ. We solve the perturbation problem for this solution, finding the independently propagating towers of states in terms of superpositions of gravitons, photons, and dilatons and their associated effective potentials. These potentials describe modes obeying conformal quantum mechanics, with couplings that we compute, and can be recast as giving the spectrum of the effective masses of the modes. By dictating the conformal weights of boundary operators, this spectrum provides crucial data for any future construction of a holographic dual to these AdS2 × S2 configurations.

New AdS2 supergravity duals of 4d SCFTs with defects

We construct new families of AdS2× S2× S2 solutions with 4 supercharges in Type II supergravities. We show that subclasses of these solutions can be interpreted in terms of defect branes embedded in 4d $$ \mathcal{N} $$ N = 4 SYM, or orbifolds thereof. This is explicitly realised by showing that the solutions asymptote locally to AdS5× S5/ℤn, in Type IIB, or its T-dual background, in Type IIA. The latter is a Gaiotto-Maldacena geometry realised on an intersection of D4 and NS5 branes. We extend the Type IIA solutions to include D6 branes, and interpret them as describing backreacted baryon vertices within 4d $$ \mathcal{N} $$ N = 2 CFTs living in D4-NS5-D6 intersections. We propose explicit quiver quantum mechanics in which the defect branes play the role of colour branes, with the D4 branes of the D4-NS5-D6 intersection becoming flavour branes. These quivers are used to compute the degeneracies of the ground states of the dual super conformal quantum mechanics, that are shown to agree with the holographic expressions.

Vacuum thermal effects in flat space-time from conformal quantum mechanics

The generators of radial conformal symmetries in Minkowski space-time can be mapped to the generators of time evolution in conformal quantum mechanics. Within this correspondence we show that in conformal quantum mechanics the state associated to the inertial vacuum in Minkowski space-time has the structure of a thermofield double. Such state is built from a bipartite “vacuum state”, the ground state of the generators of hyperbolic time evolution, which cover only part of the time domain. When time evolution is restricted to a finite time domain one obtains the temperature perceived by static diamond observers in the Minkowski vacuum. When time evolution is determined by dilations, covering only half of the time line, the temperature of the thermofield double corresponds to the non-vanishing temperature perceived by Milne observers whose proper time evolution is confined to the future cone (Milne universe) of Minkowski space-time. The two pictures are related by a conformal transformation on the real line. Our result provides a purely group theoretical derivation of the Milne and diamond temperatures and shows that the fundamental ingredient for vacuum thermal effects is the presence of a horizon rather than acceleration.

New AdS2 backgrounds and $$ \mathcal{N} $$ = 4 conformal quantum mechanics

We present a new infinite family of Type IIB backgrounds with an AdS2 factor, preserving $$ \mathcal{N} $$ N = 4 SUSY. For each member of the family we propose a precise dual Super Conformal Quantum Mechanics (SCQM). We provide holographic expressions for the number of vacua (the “central charge”), Chern-Simons terms and other non-perturbative aspects of the SCQM. We relate the “central charge” of the one-dimensional system with a combination of electric and magnetic fluxes in Type IIB. The Ramond-Ramond fluxes are used to propose an extremisation principle for the central charge. Other physical and geometrical aspects of these conformal quantum mechanics are analysed.