Publications

Order by: publication date number of citations

• Codimension-2 defects and higher symmetries in (3+1)D topological phases

  Maissam Barkeshli, Yu-An Chen, Sheng-Jie Huang, Ryohei Kobayashi, Nathanan Tantivasadakarn, Guanyu Zhu

  SciPost Phys. 14, 065 (2023) · published 11 April 2023 | Toggle abstract · pdf

  (3+1)D topological phases of matter can host a broad class of non-trivial topological defects of codimension-1, 2, and 3, of which the well-known point charges and flux loops are special cases. The complete algebraic structure of these defects defines a higher category, and can be viewed as an emergent higher symmetry. This plays a crucial role both in the classification of phases of matter and the possible fault-tolerant logical operations in topological quantum error-correcting codes. In this paper, we study several examples of such higher codimension defects from distinct perspectives. We mainly study a class of invertible codimension-2 topological defects, which we refer to as twist strings. We provide a number of general constructions for twist strings, in terms of gauging lower dimensional invertible phases, layer constructions, and condensation defects. We study some special examples in the context of $\mathbb{Z}_2$ gauge theory with fermionic charges, in $\mathbb{Z}_2 \times \mathbb{Z}_2$ gauge theory with bosonic charges, and also in non-Abelian discrete gauge theories based on dihedral ($D_n$) and alternating ($A_6$) groups. The intersection between twist strings and Abelian flux loops sources Abelian point charges, which defines an $H^4$ cohomology class that characterizes part of an underlying 3-group symmetry of the topological order. The equations involving background gauge fields for the 3-group symmetry have been explicitly written down for various cases. We also study examples of twist strings interacting with non-Abelian flux loops (defining part of a non-invertible higher symmetry), examples of non-invertible codimension-2 defects, and examples of the interplay of codimension-2 defects with codimension-1 defects. We also find an example of geometric, not fully topological, twist strings in (3+1)D $A_6$ gauge theory.

  10 citations

• Supersymmetric ground states of 3d $\mathcal{N}=4$ SUSY gauge theories and Heisenberg algebras

  Andrea E. V. Ferrari

  SciPost Phys. 14, 063 (2023) · published 6 April 2023 | Toggle abstract · pdf

  We consider 3d $\mathcal{N}=4$ theories on the geometry $\Sigma \times \mathbb{R}$, where $\Sigma$ is a closed and connected Riemann surface, from the point of view of a quantum mechanics on $\mathbb{R}$. Focussing on the elementary mirror pair in the presence of real deformation parameters, namely SQED with one hypermultiplet (SQED[1]) and the free hypermulitplet, we study the algebras of local operators in the respective quantum mechanics as well as their action on the vector space of supersymmetric ground states. We demonstrate that the algebras can be described in terms of Heisenberg algebras, and that they act in a way reminiscent of Segal-Bargmann (B-twist of the free hypermultiplet) and Nakajima (A-twist of SQED[1]) operators.

  1 citation

• Photoemission "experiments" on holographic lattices

  Filip Herček, Vladan Gecin, Mihailo Čubrović

  SciPost Phys. Core 6, 027 (2023) · published 6 April 2023 | Toggle abstract · pdf

  We construct a 2D holographic ionic lattice with hyperscaling-violating infrared geometry and study single-electron spectral functions ("ARPES photoemission curves") on this background. The spectra typically show a three-peak structure, where the central peak undergoes a crossover from a sharp but not Fermi-liquid-like quasiparticle to a wide incoherent maximum, and the broad side peaks resemble the Hubbard bands. These findings are partially explained by a perturbative near-horizon analysis of the bulk Dirac equation. Comparing the holographic Green functions in imaginary frequency with the Green functions of the Hubbard model obtained from quantum Monte Carlo, we find that the holographic model provides a very good fit to the Hubbard Green function. However, the information loss when transposing the holographic Green functions to imaginary frequencies implies that a deeper connection to Hubbard-like models remains questionable.

  2 citations

• Cost of holographic path integrals

  Ammanamanchi Ramesh Chandra, Jan de Boer, Mario Flory, Michal P. Heller, Sergio Hörtner, Andrew Rolph

  SciPost Phys. 14, 061 (2023) · published 5 April 2023 | Toggle abstract · pdf

  We consider proposals for the cost of holographic path integrals. Gravitational path integrals within finite radial cutoff surfaces have a precise map to path integrals in $T\overline{T}$ deformed holographic CFTs. In Nielsen's geometric formulation cost is the length of a not-necessarily-geodesic path in a metric space of operators. Our cost proposals differ from holographic state complexity proposals in that (1) the boundary dual is cost, a quantity that can be 'optimised' to state complexity, (2) the set of proposals is large: all functions on all bulk subregions of any co-dimension which satisfy the physical properties of cost, and (3) the proposals are by construction UV-finite. The optimal path integral that prepares a given state is that with minimal cost, and cost proposals which reduce to the CV and CV2.0 complexity conjectures when the path integral is optimised are found, while bounded cost proposals based on gravitational action are not found. Related to our analysis of gravitational action-based proposals, we study bulk hypersurfaces with a constant intrinsic curvature of a specific value and give a Lorentzian version of the Gauss-Bonnet theorem valid in the presence of conical singularities.

  5 citations

• Scrambling under quench

  Adith Sai Aramthottil, Diptarka Das, Suchetan Das, Bidyut Dey

  SciPost Phys. Core 6, 021 (2023) · published 28 March 2023 | Toggle abstract · pdf

  We evaluate out of time ordered correlators in certain low dimensional quantum systems at zero temperature, subjected to homogenous quantum quenches. We find that when the Lyapunov exponent exists, it can be identified with the quenched energy. We show that the exponent naturally gets related to the post-quench effective temperature. In the context of sudden quenches the exponent is determined in terms of the quench amplitude while for smooth quenches we observe scalings (both the Kibble-Zurek as well as the fast) of the exponent with the quench rate. The scalings are identical to that of the energy generated during the quench.

  2 citations

• Quantum chaos in perturbative super-Yang-Mills Theory

  Tristan McLoughlin, Raul Pereira, Anne Spiering

  SciPost Phys. 14, 049 (2023) · published 27 March 2023 | Toggle abstract · pdf

  We provide numerical evidence that the perturbative spectrum of anomalous dimensions in maximally supersymmetric $SU(N)$ Yang-Mills theory is chaotic at finite values of $N$. We calculate the probability distribution of one-loop level spacings for subsectors of the theory and show that for large $N$ it is given by the Poisson distribution of integrable models, while at finite values it is the Wigner-Dyson distribution of the Gaussian orthogonal ensemble random matrix theory. We extend these results to two-loop order and to a one-parameter family of deformations. We further study the spectral rigidity for these models and show that it is also well described by random matrix theory. Finally we demonstrate that the finite-$N$ eigenvectors possess properties of chaotic states.

  2 citations

• Diagonal fields in critical loop models

  Sylvain Ribault

  SciPost Phys. Core 6, 020 (2023) · published 27 March 2023 | Toggle abstract · pdf

  In critical loop models, there exist diagonal fields with arbitrary conformal dimensions, whose $3$-point functions coincide with those of Liouville theory at $c\leq 1$. We study their $N$-point functions, which depend on the $2^{N-1}$ weights of topologically inequivalent loops on a sphere with $N$ punctures. Using a numerical conformal bootstrap approach, we find that $4$-point functions decompose into infinite but discrete linear combinations of conformal blocks. We conclude that diagonal fields belong to an extension of the $O(n)$ model.

  2 citations

• The propagator matrix reloaded

  João F. Melo

  SciPost Phys. Core 6, 019 (2023) · published 24 March 2023 | Toggle abstract · pdf

  The standard way to perform calculations for quantum field theories involves the S-matrix and the assumption that the theory is free at past and future infinity. However, this assumption may not hold for field theories in non-trivial backgrounds such as curved spacetimes or finite temperature. In fact, even in the simple case of finite temperature Minkowski spacetime, there are a lot of misconceptions and confusion in the literature surrounding how to correctly take interactions into account when setting up the initial conditions. The objective of this work is to clear up these misconceptions and provide a clean and simple derivation of a formalism which includes interactions in the initial conditions and assesses whether or not it is legitimate to ignore them. The ultimate conclusion is that we cannot ignore them: quantum field theories at finite temperature are not free in the infinite past.

• Dynamically restoring conformal invariance in (integrable) $\sigma$-models

  Rigers Aliaj, Konstantinos Sfetsos, Konstantinos Siampos

  SciPost Phys. 14, 043 (2023) · published 21 March 2023 | Toggle abstract · pdf

  Integrable $\lambda$-deformed $\sigma$-models are characterized by an underlying current algebra/coset model CFT deformed, at the infinitesimal level, by current/parafermion bilinears. We promote the deformation parameters to dynamical functions of time introduced as an extra coordinate. It is conceivable that by appropriately constraining them, the beta-functions vanish and consequently the $\sigma$-model stays conformal. Remarkably, we explicitly materialize this scenario in several cases having a single and even multiple deformation parameters. These generically obey a system of non-linear second-order ordinary differential equations. They are solved by the fixed points of the RG flow of the original $\sigma$-model. Moreover, by appropriately choosing initial conditions we may even interpolate between the RG fixed points as the time varies from the far past to the far future. Finally, we present an extension of our analysis to the Yang--Baxter deformed PCMs.

• Lifshitz symmetry: Lie algebras, spacetimes and particles

  José Figueroa-O'Farrill, Ross Grassie, Stefan Prohazka

  SciPost Phys. 14, 035 (2023) · published 15 March 2023 | Toggle abstract · pdf

  We study and classify Lie algebras, homogeneous spacetimes and coadjoint orbits (``particles'') of Lie groups generated by spatial rotations, temporal and spatial translations and an additional scalar generator. As a first step we classify Lie algebras of this type in arbitrary dimension. Among them is the prototypical Lifshitz algebra, which motivates this work and the name "Lifshitz Lie algebras". We classify homogeneous spacetimes of Lifshitz Lie groups. Depending on the interpretation of the additional scalar generator, these spacetimes fall into three classes: 1. ($d+2$)-dimensional Lifshitz spacetimes which have one additional holographic direction; 2. ($d+1$)-dimensional Lifshitz—Weyl spacetimes which can be seen as the boundary geometry of the spacetimes in (1) and where the scalar generator is interpreted as an anisotropic dilation; 3. and $(d+1)$-dimensional aristotelian spacetimes with one scalar charge, including exotic fracton-like symmetries that generalise multipole algebras. We also classify the possible central extensions of Lifshitz Lie algebras and we discuss the homogeneous symplectic manifolds of Lifshitz Lie groups in terms of coadjoint orbits.

  5 citations