Publications

Order by: publication date number of citations

• 3d $\mathcal{N}=4$ mirror symmetry with 1-form symmetry

  Satoshi Nawata, Marcus Sperling, Hao Ellery Wang, Zhenghao Zhong

  SciPost Phys. 15, 033 (2023) · published 27 July 2023 | Toggle abstract · pdf

  The study of 3d mirror symmetry has greatly enhanced our understanding of various aspects of 3d $\mathcal{N}=4$ theories. In this paper, starting with known mirror pairs of 3d $\mathcal{N}=4$ quiver gauge theories and gauging discrete subgroups of the flavour or topological symmetry, we construct new mirror pairs with non-trivial 1-form symmetry. By providing explicit quiver descriptions of these theories, we thoroughly specify their symmetries (0-form, 1-form, and 2-group) and the mirror maps between them.

  12 citations

• Parity and spin CFT with boundaries and defects

  Ingo Runkel, Lóránt Szegedy, Gérard M. T. Watts

  SciPost Phys. 15, 207 (2023) · published 27 November 2023 | Toggle abstract · pdf

  This paper is a follow-up to [J. High Energy Phys. 06, 025 (2020)] in which two-dimensional conformal field theories in the presence of spin structures are studied. In the present paper we define four types of CFTs, distinguished by whether they need a spin structure or not in order to be well-defined, and whether their fields have parity or not. The cases of spin dependence without parity, and of parity without the need of a spin structure, have not, to our knowledge, been investigated in detail so far. We analyse these theories by extending the description of CFT correlators via three-dimensional topological field theory developed in [Nucl. Phys. B 646, 353 (2002)] to include parity and spin. In each of the four cases, the defining data are a special Frobenius algebra $F$ in a suitable ribbon fusion category, such that the Nakayama automorphism of $F$ is the identity (oriented case) or squares to the identity (spin case). We use the TFT to define correlators in terms of $F$ and we show that these satisfy the relevant factorisation and single-valuedness conditions. We allow for world sheets with boundaries and topological line defects, and we specify the categories of boundary labels and the fusion categories of line defect labels for each of the four types. The construction can be understood in terms of topological line defects as gauging a possibly non-invertible symmetry. We analyse the case of a $\mathbb{Z}_2$-symmetry in some detail and provide examples of all four types of CFT, with Bershadsky-Polyakov models illustrating the two new types.

  12 citations

• A model of persistent breaking of continuous symmetry

  Noam Chai, Anatoly Dymarsky, Mikhail Goykhman, Ritam Sinha, Michael Smolkin

  SciPost Phys. 12, 181 (2022) · published 1 June 2022 | Toggle abstract · pdf

  We consider a UV-complete field-theoretic model in general dimensions, including $d=2+1$, that exhibits spontaneous breaking of continuous symmetry, persisting to arbitrarily large temperatures. Our model consists of two copies of the long-range vector models, with $O(m)$ and $O(N-m)$ global symmetry groups, perturbed by double-trace operators. Using conformal perturbation theory we find weakly-coupled IR fixed points for $N\geq 6$ that reveal a spontaneous breaking of global symmetry. Namely, at finite temperature the lower rank group is broken, with the pattern persisting at all temperatures due to scale-invariance. We provide evidence that the models in question are unitary and invariant under full conformal symmetry. Our work generalizes recent results, which considered the particular case of $m=1$ and reported persistent breaking of the discrete $\mathbb{Z}_2=O(1)$. Furthermore, we show that this model exhibits a continuous family of weakly interacting field theories at finite $N$.

  12 citations

• Gauging Lie group symmetry in (2+1)d topological phases

  Meng Cheng, Po-Shen Hsin, Chao-Ming Jian

  SciPost Phys. 14, 100 (2023) · published 9 May 2023 | Toggle abstract · pdf

  We present a general algebraic framework for gauging a 0-form compact, connected Lie group symmetry in (2+1)d topological phases. Starting from a symmetry fractionalization pattern of the Lie group $G$, we first extend $G$ to a larger symmetry group $\tilde{G}$, such that there is no fractionalization with respect to $\tilde{G}$ in the topological phase, and the effect of gauging $\tilde{G}$ is to tensor the original theory with a $\tilde{G}$ Chern-Simons theory. To restore the desired gauge symmetry, one then has to gauge an appropriate one-form symmetry (or, condensing certain Abelian anyons) to obtain the final result. Studying the consistency of the gauging procedure leads to compatibility conditions between the symmetry fractionalization pattern and the Hall conductance. When the gauging can not be consistently done (i.e. the compatibility conditions can not be satisfied), the symmetry $G$ with the fractionalization pattern has an 't Hooft anomaly and we present a general method to determine the (3+1)d topological term for the anomaly. We provide many examples, including projective simple Lie groups and unitary groups to illustrate our approach.

  12 citations

• On the flow of states under $T\overline{T}$

  Jorrit Kruthoff, Onkar Parrikar

  SciPost Phys. 9, 078 (2020) · published 20 November 2020 | Toggle abstract · pdf

  We study the $T\overline{T}$ deformation of two dimensional quantum field theories from a Hamiltonian point of view, focusing on aspects of the theory in Lorentzian signature. Our starting point is a simple rewriting of the spatial integral of the $T\overline{T}$ operator, which directly implies the deformed energy spectrum of the theory. Using this rewriting, we then derive flow equations for various quantities in the deformed theory, such as energy eigenstates, operators, and correlation functions. On the plane, we find that the deformation merely has the effect of implementing successive canonical/Bogoliubov transformations along the flow. This leads us to define a class of non-local, 'dressed' operators (including a dressed stress tensor) which satisfy the same commutation relations as in the undeformed theory. This further implies that on the plane, the deformed theory retains its symmetry algebra, including conformal symmetry, if the original theory is a CFT. On the cylinder the $T\overline{T}$ deformation is much more non-trivial, but even so, correlation functions of certain dressed operators are integral transforms of the original ones. Finally, we propose a tensor network interpretation of our results in the context of AdS/CFT.

  12 citations

• An effective field theory of magneto-elasticity

  Shashin Pavaskar, Riccardo Penco, Ira Z. Rothstein

  SciPost Phys. 12, 155 (2022) · published 11 May 2022 | Toggle abstract · pdf

  We utilize the coset construction to derive the effective field theory of magnon-phonon interactions in (anti)-ferromagnetic and ferrimagnetic insulating materials. The action is used to calculate the equations of motion which generalize the Landau-Lifshitz and stress equations to allow for magneto-acoustic couplings to all orders in the fields at lowest order in the derivative expansion. We also include the symmetry breaking effects due to Zeeman, and Dzyaloshinsky-Moriya interactions. This effective theory is a toolbox for the study of magneto-elastic phenomena from first principles. As an example we use this theory to calculate the leading order contribution to the magnon decay width due to its the decay into phonons.

  12 citations

• A symmetry principle for gauge theories with fractons

  Yuji Hirono, Minyoung You, Stephen Angus, Gil Young Cho

  SciPost Phys. 16, 050 (2024) · published 20 February 2024 | Toggle abstract · pdf

  Fractonic phases are new phases of matter that host excitations with restricted mobility. We show that a certain class of gapless fractonic phases are realized as a result of spontaneous breaking of continuous higher-form symmetries whose conserved charges do not commute with spatial translations. We refer to such symmetries as nonuniform higher-form symmetries. These symmetries fall within the standard definition of higher-form symmetries in quantum field theory, and the corresponding symmetry generators are topological. Worldlines of particles are regarded as the charged objects of 1-form symmetries, and mobility restrictions can be implemented by introducing additional 1-form symmetries whose generators do not commute with spatial translations. These features are realized by effective field theories associated with spontaneously broken nonuniform 1-form symmetries. At low energies, the theories reduce to known higher-rank gauge theories such as scalar/vector charge gauge theories, and the gapless excitations in these theories are interpreted as Nambu-Goldstone modes for higher-form symmetries. Due to the nonuniformity of the symmetry, some of the modes acquire a gap, which is the higher-form analogue of the inverse Higgs mechanism of spacetime symmetries. The gauge theories have emergent nonuniform magnetic symmetries, and some of the magnetic monopoles become fractonic. We identify the 't Hooft anomalies of the nonuniform higher-form symmetries and the corresponding bulk symmetry-protected topological phases. By this method, the mobility restrictions are fully determined by the choice of the commutation relations of charges with translations. This approach allows us to view existing (gapless) fracton models such as the scalar/vector charge gauge theories and their variants from a unified perspective and enables us to engineer theories with desired mobility restrictions.

  12 citations

• A definition of primary operators in $J\bar T$-deformed CFTs

  Monica Guica

  SciPost Phys. 13, 045 (2022) · published 1 September 2022 | Toggle abstract · pdf

  $J\bar T$-deformed CFTs provide an interesting example of non-local, yet UV-complete two-dimensional QFTs that are entirely solvable. They have been recently shown to possess an infinite set of symmetries, which are a continuous deformation of the Virasoro-Kac-Moody symmetries of the seed CFT. In this article, we put forth a definition of primary operators in $J\bar T$-deformed CFTs on a cylinder, which are singled out by having CFT-like momentum-space commutation relations with the symmetry generators in the decompatification limit. We show -- based on results we first derive for the case of $J^1 \wedge J^2$-deformed CFTs -- that all correlation functions of such operators in the $J\bar T$-deformed CFT can be computed exactly in terms of the correlation functions of the undeformed CFT and are crossing symmetric in the plane limit. In particular, two and three-point functions are simply given by the corresponding momentum-space correlator in the undeformed CFT, with all dimensions replaced by particular momentum-dependent conformal dimensions. Interestingly, scattering amplitudes off the near-horizon of extremal black holes are known to take a strikingly similar form.

  12 citations

• Squashing and supersymmetry enhancement in three dimensions

  Joseph Minahan, Usman Naseer, Charles Thull

  SciPost Phys. 12, 025 (2022) · published 17 January 2022 | Toggle abstract · pdf

  We consider mass-deformed theories with ${\cal N}\geq2$ supersymmetry on round and squashed three-spheres. By embedding the supersymmetric backgrounds in extended supergravity we show that at special values of mass deformations the supersymmetry is enhanced on the squashed spheres. When the $3d$ partition function can be obtained by a limit of a $4d$ index we also show that for these special mass deformations only the states annihilated by extra supercharges contribute to the index. By using an equivalence between partition functions on squashed spheres and ellipsoids, we explain the recently observed squashing independence of the partition function of mass-deformed ABJ(M) theory on the ellipsoid. We provide further examples of such simplification for various $3d$ supersymmetric theories.

  12 citations

• A roadmap for bootstrapping critical gauge theories: decoupling operators of conformal field theories in $d>2$ dimensions

  Yin-Chen He, Junchen Rong, Ning Su

  SciPost Phys. 11, 111 (2021) · published 22 December 2021 | Toggle abstract · pdf

  We propose a roadmap for bootstrapping conformal field theories (CFTs) described by gauge theories in dimensions $d>2$. In particular, we provide a simple and workable answer to the question of how to detect the gauge group in the bootstrap calculation. Our recipe is based on the notion of \emph{decoupling operator}, which has a simple (gauge) group theoretical origin, and is reminiscent of the null operator of $2d$ Wess-Zumino-Witten CFTs in higher dimensions. Using the decoupling operator we can efficiently detect the rank (i.e. color number) of gauge groups, e.g., by imposing gap conditions in the CFT spectrum. We also discuss the physics of the equation of motion, which has interesting consequences in the CFT spectrum as well. As an application of our recipes, we study a prototypical critical gauge theory, namely the scalar QED which has a $U(1)$ gauge field interacting with critical bosons. We show that the scalar QED can be solved by conformal bootstrap, namely we have obtained its kinks and islands in both $d=3$ and $d=2+\epsilon$ dimensions.

  12 citations