arXiv subjects

Trivko Kukolj

Publications and source records attributed to Trivko Kukolj.

5 recordsLinked to original sources

arXiv2026

q-Askey Deformations of Double-Scaled SYK

We construct families of deformations of the double-scaled SYK (DSSYK) model and investigate their bulk interpretation. We introduce microscopic deformations of the SYK model which, after ensemble averaging and in the double-scaling limit, are described by a transfer matrix encoding the recurrence relations of basic orthogonal polynomials in the q-Askey scheme. For certain families of deformations in the semiclassical limit at finite temperature, the chord number (encoding Krylov complexity) corresponds to the length of an Einstein-Rosen bridge connecting an End-Of-The-World brane to an anti-de Sitter asymptotic boundary. By increasing one of the deformation parameters, the models eventually exhibit discrete energy levels, signaling a new geometric transition in sine dilaton gravity. Via the SYK-Schur duality, Krylov complexity also admits a representation-theoretic interpretation as the spread of the SU(2) spin in the index of an $\mathcal{N}=2$ SU(2) gauge theory. We study the operator algebras of the deformed theories. The algebras can be type II$_1$ or type I$_\infty$ factors, depending on the operators that are included. The entanglement entropy between the type II$_1$ algebras for a pure state manifests as an extremal surface through the Ryu-Takayanagi formula. We discuss connections between our results and the emergence of baby universes in the bulk.

hep-th↗

arXiv2025

Comments on Class S(YK)

We present a DSSYK-like interpretation of the Schur half-indices of $\mathcal{N}=2$ $SU(2)$ gauge theories with matter, in the presence of fundamental Wilson lines. The Schur half-indices of these theories can be understood as transition amplitudes in a non-vacuum sector of ordinary DSSYK. In the language of chord diagrams, the half-indices are obtained by summing over diagrams with special segments, which correspond to coherent states of the $q$-oscillator algebra. In addition, we show that the Schur half-index of $SU(2)$ gauge theory with $n_F=4$ fundamental half-hypermultiplets corresponds to the partition function of a particle on the quantum disk.

hep-th↗

arXiv2024

Four-point functions and contact terms from higher-spin Ward identities of Chern-Simons-matter theory

Large $N$ quasifermionic ($QF$) Chern-Simons-matter theories exhibit weakly-broken higher-spin symmetry and contain an infinite-dimensional algebra of almost-conserved higher-spin currents. By analyzing local higher-spin Ward identities, we constrain the higher-spin algebra of this theory, for operators of spin $s<4$. The solution interpolates smoothly between Ward identities of free-fermionic and critical-bosonic $U(N)$ models, in accordance with the bosonization duality. At finite 't Hooft coupling, we decompose four-point current correlators involving $(\partial\cdot J_3)^{QF}$ in terms of free theory structures and identify possible epsilon-transform relations for $QF$ four-point functions. Additionally, we find that higher correlators of the theory develop scheme-independent higher-spin contact terms, stemming from the presence of a background Chern-Simons term in the effective action. These terms are related to similar contact terms of the associated quasibosonic Chern-Simons-matter theory via Legendre transform. The results are supplemented by perturbative checks, including collinear limit computations of $\langle T_{--}J_+J_+\rangle_{QF}$, $\langle T_{--}J_+J_+O\rangle_{QF}$ and $\langle J_{-{}-{}-}J_+J_+J_+\rangle_{QF}$.

hep-th↗

arXiv2024

A chiral limit for Chern-Simons-matter theories

Large N quasi-fermionic Chern-Simons-matter theories have an approximate higher-spin symmetry that strongly constrains their correlation functions. In particular, the 3-point functions for generic spins are combinations of 3 structures (with specific dependence on the positions and helicities), and the coupling-dependence of the coefficient of each structure is uniquely determined. In the past few years, several relations between different structures were found. In this paper we show that all the relations between the structures follow from (or, conversely, they imply) a specific form written by Skvortsov for the vertices of the dual higher-spin gravity theory on four-dimensional anti-de Sitter space, when written in spinor-helicity variables. The dual bulk theory has a specific limit where it simplifies and becomes a "chiral higher-spin gravity theory", and we discuss what can be said about this limit in the dual Chern-Simons-matter theories, where it involves an analytic continuation to complex couplings.

hep-th↗

arXiv2019

Spontaneous isotropy breaking for vortices in nonlinear left-handed metamaterials

We explore numerically and analytically the pattern formation and symmetry breaking of beams propagating through left-handed (negative) nonlinear metamaterials. When the input beam is a vortex with topological charge (winding number) $Q$, the initially circular (isotropic) beam acquires the symmetry of a polygon with $Q$, $2Q$ or $3Q$ sides, depending on the details of the response functions of the material. Within an effective field-theory model, this phenomenon turns out to be a case of spontaneous dynamical symmetry breaking described by a Landau-Ginzburg functional. Complex nonlinear dependence of the magnetic permittivity on the magnetic field of the beam plays a central role, as it introduces branch cuts in the mean-field solution, and permutations among different branches give rise to discrete symmetries of the patterns. By considering loop corrections in the effective Landau-Ginzburg field theory we obtain reasonably accurate predictions of the numerical results.

physics.optics↗