arXiv subjects

Anton Kapustin

Publications and source records attributed to Anton Kapustin.

At least 55 records · Page 3Linked to original sources

arXiv2015

Fermionic Symmetry Protected Topological Phases and Cobordisms

It has been proposed recently that interacting Symmetry Protected Topological (SPT) phases can be classified using cobordism theory. We test this proposal in the case of fermionic SPT phases with Z/2 symmetry, where Z/2 is either time-reversal or an internal symmetry. We find that cobordism classification correctly describes all known fermionic SPT phases in space dimension less than or equal to 3 and also predicts that all such phases can be realized by free fermions. In higher dimensions we predict the existence of inherently interacting fermionic SPT phases.

cond-mat.str-el↗

arXiv2015

Equivariant Topological Quantum Field Theory and Symmetry Protected Topological Phases

Short-range entangled topological phases of matter are closely connected to Topological Quantum Field Theory. We use this connection to classify bosonic Symmetry Protected Topological Phases in low dimensions, including the case when the symmetry involves time-reversal. To accomplish this, we generalize Turaev's description of equivariant TQFT to the unoriented case. We show that invertible unoriented equivariant TQFTs in one or less spatial dimensions are classified by twisted group cohomology, in agreement with the group cohomology proposal of Chen, Gu, Liu and Wen. We also show that invertible oriented equivariant TQFTs in spatial dimension two or less are classified by ordinary group cohomology.

cond-mat.str-el↗

arXiv2015

Higher symmetry and gapped phases of gauge theories

We study topological field theory describing gapped phases of gauge theories where the gauge symmetry is partially Higgsed and partially confined. The TQFT can be formulated both in the continuum and on the lattice and generalizes Dijkgraaf-Witten theory by replacing a finite group by a finite 2-group. The basic field in this TQFT is a 2-connection on a principal 2-bundle. We classify topological actions for such theories as well as loop and surface observables. When the topological action is trivial, the TQFT is related to a Dijkgraaf-Witten theory by electric-magnetic duality, but in general it is distinct. We propose the existence of new phases of matter protected by higher symmetry.

hep-th↗

arXiv2015

Generalized Global Symmetries

A $q$-form global symmetry is a global symmetry for which the charged operators are of space-time dimension $q$; e.g. Wilson lines, surface defects, etc., and the charged excitations have $q$ spatial dimensions; e.g. strings, membranes, etc. Many of the properties of ordinary global symmetries ($q$=0) apply here. They lead to Ward identities and hence to selection rules on amplitudes. Such global symmetries can be coupled to classical background fields and they can be gauged by summing over these classical fields. These generalized global symmetries can be spontaneously broken (either completely or to a subgroup). They can also have 't Hooft anomalies, which prevent us from gauging them, but lead to 't Hooft anomaly matching conditions. Such anomalies can also lead to anomaly inflow on various defects and exotic Symmetry Protected Topological phases. Our analysis of these symmetries gives a new unified perspective of many known phenomena and uncovers new results.

hep-th↗

arXiv2014

Bosonic Topological Insulators and Paramagnets: a view from cobordisms

We classify Bosonic Topological Insulators and Paramagnets in D<=4 spatial dimensions using the cobordism approach. For D<4 we confirm that the only such phase which does not fit into the group cohomology classification is the 3D Bosonic Topological Insulator protected by time-reversal symmetry whose surface admits an all-fermion topologically ordered state. For D=4 there is a unique "beyond group cohomology" phase. It is protected by gravitational anomalies of the boundary theory and is stable without any additional symmetry.

cond-mat.str-el↗

arXiv2014

Anomalies of discrete symmetries in various dimensions and group cohomology

We study 't Hooft anomalies for discrete global symmetries in bosonic theories in 2, 3 and 4 dimensions. We show that such anomalies may arise in gauge theories with topological terms in the action, if the total symmetry group is a nontrivial extension of the global symmetry by the gauge symmetry. Sometimes the 't Hooft anomaly for a d-dimensional theory with a global symmetry G can be canceled by anomaly inflow from a (d+1)-dimensional topological gauge theory with gauge group G. Such d-dimensional theories can live on the surfaces of Symmetry Protected Topological Phases. We also give examples of theories with more severe 't Hooft anomalies which cannot be canceled in this way.

hep-th↗

arXiv2014

Symmetry Protected Topological Phases, Anomalies, and Cobordisms: Beyond Group Cohomology

We propose that Symmetry Protected Topological Phases with a finite symmetry group G are classified by cobordism groups of the classifying space of G. This provides an explanation for the recent discovery of bosonic SPT phases which do not fit into the group cohomology classification. We discuss the connection of the cobordism classification of SPT phases to gauge and gravitational anomalies in various dimensions.

cond-mat.str-el↗

arXiv2014

Anomalies of discrete symmetries in three dimensions and group cohomology

We study 't Hooft anomalies for a global discrete internal symmetry G. We construct examples of bosonic field theories in three dimensions with a non-vanishing 't Hooft anomaly for a discrete global symmetry. We also construct field theories in three dimensions with a global discrete internal symmetry G_1 x G_2 such that gauging G_1 necessarily breaks G_2 and vice versa. This is analogous to the Adler-Bell-Jackiw axial anomaly in four dimensions and parity anomaly in three dimensions.

hep-th↗

arXiv2014

Coupling a QFT to a TQFT and Duality

We consider coupling an ordinary quantum field theory with an infinite number of degrees of freedom to a topological field theory. On R^d the new theory differs from the original one by the spectrum of operators. Sometimes the local operators are the same but there are different line operators, surface operators, etc. The effects of the added topological degrees of freedom are more dramatic when we compactify R^d, and they are crucial in the context of electric-magnetic duality. We explore several examples including Dijkgraaf-Witten theories and their generalizations both in the continuum and on the lattice. When we couple them to ordinary quantum field theories the topological degrees of freedom allow us to express certain characteristic classes of gauge fields as integrals of local densities, thus simplifying the analysis of their physical consequences.

hep-th↗

arXiv2013

Topological Field Theory on a Lattice, Discrete Theta-Angles and Confinement

We study a topological field theory describing confining phases of gauge theories in four dimensions. It can be formulated on a lattice using a discrete 2-form field talking values in a finite abelian group (the magnetic gauge group). We show that possible theta-angles in such a theory are quantized and labeled by quadratic functions on the magnetic gauge group. When the theta-angles vanish, the theory is dual to an ordinary topological gauge theory, but in general it is not isomorphic to it. We also explain how to couple a lattice Yang-Mills theory to a TQFT of this kind so that the 't Hooft flux is well-defined, and quantized values of the theta-angles are allowed. The quantized theta-angles include the discrete theta-angles recently identified by Aharony, Seiberg and Tachikawa.

hep-th↗

arXiv2013

Topological Quantum Field Theory, Nonlocal Operators, and Gapped Phases of Gauge Theories

We revisit the role of loop and surface operators as order parameters for gapped phases of four-dimensional gauge theories. We show that in some cases surface operators are confined, and that this fact can be used to distinguish phases which are not distinguished by the Wilson-'t Hooft criterion. The long-distance behavior of loop and surface operators which are neither confined nor screened is controlled by a 4d TQFT. We construct these TQFTs for phases which are characterized by the presence of electrically and/or magnetically charged condensates. Interestingly, the TQFT describing a phase with a nonabelian monopole condensate is based on the theory of nonabelian gerbes. We also show that in phases with a dyonic condensate the low-energy theta-angle is quantized.

hep-th↗

arXiv2013

Ground-state degeneracy for abelian anyons in the presence of gapped boundaries

Gapped phases with long-range entanglement may admit gapped boundaries. If the boundary is gapped, the ground-state degeneracy is well-defined and can be computed using methods of Topological Quantum Field Theory. We derive a general formula for the ground-state degeneracy for abelian Fractional Quantum Hall phases, including the cases when connected components of the boundary are subdivided into an arbitrary number of segments, with a different boundary condition on each segment, and in the presence of an arbitrary number of boundary domain walls.

cond-mat.str-el↗

arXiv2013

Is there life beyond Quantum Mechanics?

We formulate physically-motivated axioms for a physical theory which for systems with a finite number of degrees of freedom uniquely lead to Quantum Mechanics as the only nontrivial consistent theory. Complex numbers and the existence of the Planck constant common to all systems arise naturally in this approach. The axioms are divided into two groups covering kinematics and basic measurement theory respectively. We show that even if the second group of axioms is dropped, there are no deformations of Quantum Mechanics which preserve the kinematic axioms. Thus any theory going beyond Quantum Mechanics must represent a radical departure from the usual a priori assumptions about the laws of Nature.

quant-ph↗

arXiv2013

Exact results for supersymmetric abelian vortex loops in 2+1 dimensions

We define a class of supersymmetric defect loop operators in N = 2 gauge theories in 2+1 dimensions. We give a prescription for computing the expectation value of such operators in a generic N = 2 theory on the three-sphere using localization. We elucidate the role of defect loop operators in IR dualities of supersymmetric gauge theories, and write down their transformation properties under the SL(2, Z) action on conformal theories with abelian global symmetries.

hep-th↗

arXiv2013

Wilson loops in supersymmetric Chern-Simons-matter theories and duality

We study the algebra of BPS Wilson loops in 3d gauge theories with N=2 supersymmetry and Chern-Simons terms. We argue that new relations appear on the quantum level, and that in many cases this makes the algebra finite-dimensional. We use our results to propose the mapping of Wilson loops under Seiberg-like dualities and verify that the proposed map agrees with the exact results for expectation values of circular Wilson loops. In some cases we also relate the algebra of Wilson loops to the equivariant quantum K-ring of certain quasi projective varieties. This generalizes the connection between the Verlinde algebra and the quantum cohomology of the Grassmannian found by Witten.

hep-th↗

arXiv2012

Remarks on nonrelativistic Goldstone bosons

We discuss excitations in nonrelativistic field theories with spontaneous breaking of a continuous global symmetry. It is known that in such systems there are two types of Goldstone bosons (Type A and Type B) whose dispersion law is generically linear or quadratic, respectively. We show that Type B Goldstone bosons may have gapped partners which we call almost-Goldstone bosons. With some nondegeneracy assumption about the low-energy effective action, the total number of Goldstone and almost-Goldstone bosons adds up to the number of broken symmetry generators. We propose that deviations of the dispersion law of Goldstone bosons from linearity at small momenta may serve as a signature of small breaking of time-reversal symmetry.

hep-ph↗

arXiv2011

Dualities for 3d Theories with Tensor Matter

We study dualities for ${\cal N}=2$ 3d Chern-Simons matter theories with gauge groups U/Sp/O, matter in the two-index tensor representations (adjoint/symmetric/antisymmetric) in addition to the fundamental representation, and a superpotential. These dualities are analogous to Kutasov-Schwimmer-Seiberg dualities in 4d. We test them by computing the superconformal index and the partition function on $S^3$ for many dual pairs and find perfect agreement. In some cases we find a simple dual description for theories with tensor matter and no superpotential, thereby generalizing the "Duality Appetizer" of Jafferis and Yin to an infinite class of theories. We also investigate nonperturbative truncation of the chiral ring proposed in the context of 4d dualities.

hep-th↗

arXiv2011

Generalized Superconformal Index for Three Dimensional Field Theories

We introduce a generalization of the S^2 x S^1 superconformal index where background gauge fields with magnetic flux are coupled to the global symmetries of the theory. This allows one to gauge a global symmetry at the level of the index, which we use to show the matching of the superconformal index for N=2 SQED with N_f flavors and its mirror dual.

hep-th↗