Vaibhav Gautam

We consider the partially-deconfined saddle of large-N pure Yang-Mills theory lying between confined and deconfined phases, in which the color degrees of freedom split into confined and deconfined sectors. Based on the microscopic mechanism of deconfinement, we argue that a flux tube is formed in the confined sector and a linear confinement potential is generated. The string tension should not depend on the size of the confined sector. We provide evidence for the case of the finite-temperature strong-coupling lattice gauge theory. In particular, we make analytic predictions assuming linear confinement in the confined sector, and then confirm these by numerical simulations. We discuss some implications of the conjecture to QCD and holography.

In this paper we initiate the study of form factors for the massless scattering of integrable AdS₂ superstrings, where the difference-form of the S-matrix can be exploited to implement the relativistic form factor bootstrap. The non-standard nature of the S-matrix implies that traditional methods do not apply. We use the fact that the massless AdS₂ S-matrix is a limit of a better-behaved S-matrix found by Fendley. We show that the previously conjectured massless AdS₂ dressing factor coincides with the limit of the De Martino-Moriconi improved dressing factor for the Fendley S-matrix. We then solve the form factor constraints in the two-particle case. Along the way we find a method to construct integral representations of relativistic dressing factors satisfying specific assumptions, and use it to obtain analytic proofs of crossing and unitarity relations.

We study the boundary integrability problem of the massless sector of AdS₃ × S³ × T⁴ string theory. We obtain the massless reflection matrices for all the possible boundary coideal subalgebras-singlet and vector representations, right and left boundary-and check basic properties of our solutions, primarily the boundary Yang-Baxter equation in all possible combinations of scattering particles. We exploit the difference-form of the massless scattering theory to find a very simple and exhaustive list of reflection matrices. *

In gauge/gravity duality, matrix degrees of freedom on the gauge theory side play important roles for the emergent geometry. In this paper, we discuss how the entanglement on the gravity side can be described as the entanglement between matrix degrees of freedom. Our approach, which we call "matrix entanglement', is different from "target space entanglement' proposed and discussed recently by several groups. We consider several classes of quantum states to which our approach can play important roles. When applied to fuzzy sphere, matrix entanglement can be used to define the usual spatial entanglement in two-brane or five-brane world-volume theory nonperturbatively in a regularized setup. Another application is to a small black hole in AdS5xS5 that can evaporate without being attached to a heat bath, for which our approach suggests a gauge theory origin of the Page curve. The confined degrees of freedom in the partially-deconfined states play the important roles.