Two-dimensional Field Theory Research Articles

Dilaton shifts, probability measures, and decomposition

Abstract In this paper we discuss dilaton shifts (Euler counterterms) arising in decomposition of two-dimensional quantum field theories with higher-form symmetries. Relative shifts between universes are fixed by locality and take a universal form, reflecting underlying (noninvertible, quantum) symmetries. The first part of this paper constructs a general formula for such dilaton shifts, and discusses related computations. In the second part of this paper, we comment on the relation between decomposition and ensembles.

Noninvertible symmetries in 2D from type IIB string theory

We propose a top-down approach to noninvertible symmetries in two-dimensional quantum field theories and their three-dimensional (3D) associated symmetry topological field theories. We focus on the gauge theory engineered on D1-branes probing a particular Calabi-Yau 4-fold singularity. We show how to derive the symmetry topological field theory, a 3D Dijkgraaf-Witten theory, from the IIB supergravity under dimensional reduction. We also identify branes behind the noninvertible topological lines by dimensionally reducing their world volume actions. The action of noninvertible lines on charged local operators is then realized as the Hanany-Witten transition. Published by the American Physical Society 2024

Determination of the flexoelectric coefficient in nematic liquid crystals by using fully leaky optical guided mode

ABSTRACT Fully leaky optical-guided mode is employed to determine the difference of the splay and bend flexoelectric coefficient e 1−e 3 in negative nematic Liquid crystal (LC) MS-N0130-000. The theoretical curves of reflected signals versus internal angle are obtained by using elastic continuum theory under two-dimensional electric field and multi-layer optical theory of LC. The experimental curves of reflected signals versus internal angle are obtained by using the fully leaky optical-guided wave technique when alternating current (AC) and direct current (DC) were applied on the Hybrid aligned nematic in-plane switching (HAN-IPS) LC cell respectively. The approximate value of the flexoelectric coefficient e 1−e 3 of MS-N01300-000 is 5.5 × 10−11C/m, which is obtained by comparing theoretical curves with experimental curves.

Geometries with twisted spheres and non-abelian T-dualities

Spectral flow in two-dimensional superconformal field theories is known to correspond to a geometrical mixing between two circles in the gravity dual. We generalize this operation to the geometries which have SO(k+1)×SO(k+1) isometries with k > 1 and perform various non-abelian T-dualities of the resulting twisted backgrounds. Combination of non-abelian twists and dualities leads to a new solution generating technique in supergravity, and we apply it to the geometries dual to supersymmetric states in \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal{N}$$\\end{document} = 4 super-Yang-Mills theory.

Spontaneous symmetry breaking on surface defects

Coleman’s theorem states that continuous internal symmetries cannot be spontaneously broken in two-dimensional quantum field theories (QFTs). In this work we consider surface (i.e. two-dimensional) defects in d-dimensional conformal field theories (CFTs) invariant under a continuous internal symmetry group G. We study under which conditions it is possible for a surface defect to break spontaneously a continuous internal symmetry. We find that spontaneous symmetry breaking (SSB) is impossible under reasonable assumptions on the defect Renormalization Group (RG) flow. Counterexamples are possible only for exotic RG flows, that do not terminate at a fixed-point. We discuss an example of this kind. We also illustrate our no-go result with an effective field theory analysis of generic defect RG flows. We find a generic weakly coupled defect universality class (with no SSB), where correlation functions decay logarithmically. Our analysis generalizes the recent discovery by Metlitski of the extraordinary-log boundary universality class in the O(N) model.

Finite volume form factors in integrable theories

We develop a new method to calculate finite size corrections for form factors in two-dimensional integrable quantum field theories. We extract these corrections from the excited state expectation value of bilocal operators in the limit when the operators are far apart. We elaborate the finite size effects explicitly up to the 3rd Lüscher order and conjecture the structure of the general form. We also fully recover the explicitly known massive fermion finite volume form factors.

Towards a quadratic Poisson algebra for the subtracted classical monodromy of symmetric space sine-Gordon theories

Symmetric space sine-Gordon theories are two-dimensional massive integrable field theories, generalising the sine-Gordon and complex sine-Gordon theories. To study their integrability properties on the real line, it is necessary to introduce a subtracted monodromy matrix. Moreover, since the theories are not ultralocal, a regularisation is required to compute the Poisson algebra for the subtracted monodromy. In this article, we regularise and compute this Poisson algebra for certain configurations, and show that it can both satisfy the Jacobi identity and imply the existence of an infinite number of conserved quantities in involution.

Null energy constraints on two-dimensional RG flows

We study applications of spectral positivity and the averaged null energy condition (ANEC) to renormalization group (RG) flows in two-dimensional quantum field theory. We find a succinct new proof of the Zamolodchikov c-theorem, and derive further independent constraints along the flow. In particular, we identify a natural C-function that is a completely monotonic function of scale, meaning its derivatives satisfy the alternating inequalities (–1)nC(n)(μ2) ≥ 0. The completely monotonic C-function is identical to the Zamolodchikov C-function at the endpoints, but differs along the RG flow. In addition, we apply Lorentzian techniques that we developed recently to study anomalies and RG flows in four dimensions, and show that the Zamolodchikov c-theorem can be restated as a Lorentzian sum rule relating the change in the central charge to the average null energy. This establishes that the ANEC implies the c-theorem in two dimensions, and provides a second, simpler example of the Lorentzian sum rule.

BMS modular covariance and structure constants

Two-dimensional (2d) field theories invariant under the Bondi-Metzner-Sachs algebra, or 2d BMSFTs in short, are putative holographic duals of Einstein gravity in 3d asymptotically flat spacetimes. When defined on a torus, these field theories come equipped with a modified modular structure. We use the modular covariance of the BMS torus two-point function to develop formulae for different three-point structure constants of the field theory. These structure constants indicate that BMSFTs follow the eigenstate thermalization hypothesis, albeit with some interesting changes to usual 2d CFTs. The singularity structures of the structure constants contain information on perturbations of cosmological horizons in 3d asymptotically flat spacetimes, which we show can also be obtained as a limit of BTZ quasinormal modes.

Fermionization of fusion category symmetries in 1+1 dimensions

We discuss the fermionization of fusion category symmetries in two-dimensional topological quantum field theories (TQFTs). When the symmetry of a bosonic TQFT is described by the representation category Rep(H) of a semisimple weak Hopf algebra H, the fermionized TQFT has a superfusion category symmetry SRep(H\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{H} $$\\end{document}u), which is the supercategory of super representations of a weak Hopf superalgebra H\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{H} $$\\end{document}u. The weak Hopf superalgebra H\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{H} $$\\end{document}u depends not only on H but also on a choice of a non-anomalous ℤ2 subgroup of Rep(H) that is used for the fermionization. We derive a general formula for H\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{H} $$\\end{document}u by explicitly constructing fermionic TQFTs with SRep(H\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{H} $$\\end{document}u) symmetry. We also construct lattice Hamiltonians of fermionic gapped phases when the symmetry is non-anomalous. As concrete examples, we compute the fermionization of finite group symmetries, the symmetries of finite gauge theories, and duality symmetries. We find that the fermionization of duality symmetries depends crucially on F-symbols of the original fusion categories. The computation of the above concrete examples suggests that our fermionization formula of fusion category symmetries can also be applied to non-topological QFTs.

Mock modularity and a secondary elliptic genus

The theory of Topological Modular Forms suggests the existence of deformation invariants for two-dimensional supersymmetric field theories that are more refined than the standard elliptic genus. In this note we give a physical definition of some of these invariants. The theory of mock modular forms makes a surprise appearance, shedding light on the integrality properties of some well-known examples.

Anisotropic Scaling Non-Relativistic Holography: A Symmetry Perspective

We study the holographic dual of the two-dimensional non-relativistic field theory with anisotropic scaling from a symmetry perspective. We construct a new four-dimensional metric with two-dimensional global anisotropic scaling isometry. The four-dimensional spacetime is homogeneous and is a solution of Einstein gravity with quadratic-curvature extension. We consider this spacetime dual to the vacuum of the boundary field theory. By introducing a proper solution phase space, we find that the asymptotic symmetry of the gravity theory is the two-dimensional local anisotropic conformal symmetry, which recovers precisely the results from the dual non-relativistic field theory side.

Minimal nondegenerate extensions

We prove that every slightly degenerate braided fusion category admits a minimal nondegenerate extension, and hence that every pseudo-unitary super modular tensor category admits a minimal modular extension. This completes the program of characterizing minimal nondegenerate extensions of braided fusion categories. Our proof relies on the new subject of fusion 2 2 -categories. We study in detail the Drinfel’d centre Z ( M o d - B ) \mathcal {Z}({_{}\mathrm {Mod}\text {-}\mathcal {B}}) of the fusion 2 2 -category M o d - B {_{}\mathrm {Mod}\text {-}\mathcal {B}} of module categories of a braided fusion 1 1 -category B \mathcal {B} . We show that minimal nondegenerate extensions of B \mathcal {B} correspond to certain trivializations of Z ( M o d - B ) \mathcal {Z}({_{}\mathrm {Mod}\text {-}\mathcal {B}}) . In the slightly degenerate case, such trivializations are obstructed by a class in H 5 ( K ( Z 2 , 2 ) ; k × ) H^5(K(\mathbb {Z}_2, 2); \mathbb {k}^\times ) and we use a numerical invariant—defined by evaluating a certain two-dimensional topological field theory on a Klein bottle—to prove that this obstruction always vanishes. Along the way, we develop techniques to explicitly compute in braided fusion 2 2 -categories which we expect will be of independent interest. In addition to the model of Z ( M o d - B ) \mathcal {Z}({_{}\mathrm {Mod}\text {-}\mathcal {B}}) in terms of braided B \mathcal {B} -module categories, we develop a computationally useful model in terms of certain algebra objects in B \mathcal {B} . We construct an S S -matrix pairing for any braided fusion 2 2 -category, and show that it is nondegenerate for Z ( M o d - B ) \mathcal {Z}({_{}\mathrm {Mod}\text {-}\mathcal {B}}) . As a corollary, we identify components of Z ( M o d - B ) \mathcal {Z}({_{}\mathrm {Mod}\text {-}\mathcal {B}}) with blocks in the annular category of B \mathcal {B} and with the homomorphisms from the Grothendieck ring of the Müger centre of B \mathcal {B} to the ground field.

Topological gauging and double current deformations

We study solvable deformations of two-dimensional quantum field theories driven by a bilinear operator constructed from a pair of conserved U(1) currents Ja. We propose a quantum formulation of these deformations, based on the gauging of the corresponding symmetries in a path integral. This formalism leads to an exact dressing of the S-matrix of the system, similarly as what happens in the case of a textrm{T}overline{textrm{T}} deformation. For conformal theories the deformations under study are expected to be exactly marginal. Still, a peculiar situation might arise when the conserved currents Ja are not well-defined local operators in the original theory. A simple example of this kind of system is provided by rotation currents in a theory of multiple free, massless, non-compact bosons. We verify that, somewhat unexpectedly, such a theory is indeed still conformal after deformation and that it coincides with a TsT transformation of the original system. We then extend our formalism to the case in which the conserved currents are non-Abelian and point out its connection with Deformed T-dual Models and homogeneous Yang-Baxter deformations. In this case as well the deformation is based on a gauging of the symmetries involved and it turns out to be non-trivial only if the symmetry group admits a non-trivial central extension. Finally we apply what we learned by relating the textrm{T}overline{textrm{T}} deformation to the central extension of the two-dimensional Poincaré algebra.

Toverline{T} deformed scattering happens within matrices

We show the Toverline{T} deformation of two-dimensional quantum field theories is equivalent to replacing the spacetime dependence of the fields with dependence on the indices of infinitely large matrices. We show how this correspondence explains the CDD phase dressing of the S-matrix and the general formula for the deformation of arbitrary correlation functions. We also describe how the Moyal deformation of self-dual gravity is a Toverline{T} deformation of the theory described by the Chalmers-Siegel action, where the Toverline{T} deformation is defined on the two-dimensional plane of interactions.

Classical integrability of root- TT¯ flows

The root-$T\overline{T}$ flow was recently introduced as a universal and classically marginal deformation of any two-dimensional translation-invariant field theory. The flow commutes with the (irrelevant) $T\overline{T}$ flow, and it can be integrated explicitly for a large class of actions, leading to nonanalytic Lagrangians reminiscent of the four-dimensional modified-Maxwell theory (ModMax). It is not a priori obvious whether the root-$T\overline{T}$ flow preserves integrability, as is the case for the $T\overline{T}$ flow. In this paper we demonstrate that this is the case for a large class of classical models by explicitly constructing a deformed Lax connection. We discuss the principal chiral model and the nonlinear sigma models on symmetric and semisymmetric spaces, without or with the Wess-Zumino term. We also construct Lax connections for the two-parameter families of theories deformed by both root-$T\overline{T}$ and $T\overline{T}$ for all of these models.

Asymptotics in an asymptotic CFT

In this work we illustrate the resurgent structure of the λ-deformation; a two-dimensional integrable quantum field theory that has an RG flow with an SU(N)k Wess-Zumino-Witten conformal fixed point in the UV. To do so we use modern matched asymptotic techniques applied to the thermodynamic Bethe ansatz formulation to compute the free energy to 38 perturbative orders in an expansion of large applied chemical potential. We find numerical evidence for factorial asymptotic behaviour with both alternating and non-alternating character which we match to an analytic expression. A curiosity of the system is that the leading non-alternating factorial growth vanishing when k divides N. The ambiguities associated to Borel resummation of this series are suggestive of non-perturbative contributions. This is verified with an analytic study of the TBA system demonstrating a cancellation between perturbative and non-perturbative ambiguities.

Droplet-mediated long-range interfacial correlations. Exact field theory for entropic repulsion effects

We consider near-critical two-dimensional statistical systems at phase coexistence on the half plane with boundary conditions leading to the formation of a droplet separating coexisting phases. General low-energy properties of two-dimensional field theories are used in order to find exact analytic results for one- and two-point correlation functions of both the energy density and order parameter fields. The subleading finite-size corrections are also computed and interpreted within an exact probabilistic picture in which interfacial fluctuations are characterized by the probability density of a Brownian excursion. The explicit analysis of the closed-form expression for order parameter correlations reveals the long-ranged character of interfacial correlations and their confinement within the interfacial region. The analysis of correlations is then carried out in momentum space through the notion of interface structure factor, which we extend to the case of systems bounded by a flat wall. The presence of the wall and its associated entropic repulsion leads to a specific term in the interface structure factor which we identify.

The Hermitian axiom on two-dimensional topological quantum field theories

We examine Atiyah’s Hermitian axiom for two-dimensional complex topological quantum field theories. Building on the correspondence between 2D topological quantum field theories (TQFTs) and Frobenius algebras, we find the algebraic objects corresponding to Hermitian and unitary TQFTs, respectively, and prove structure theorems about them. We then clarify a few older results on unitary TQFTs using our structure theorems.

Seismic fragility analysis of free-spanning submarine pipelines incorporating soil spatial variability in soil-pipe interaction and offshore motion propagation

Geotechnical engineering problems are always faced with various sources of uncertainty, especially the uncertainties of soil properties. This paper presents the seismic fragility analysis of free-spanning submarine pipelines (FSSPs) with consideration of soil spatial variability. Firstly, the two-dimensional random field theory is employed to account for the spatial distribution characteristics of soil properties, and the levels of spatial variability are shifted by changing the autocorrelation lengths. Then, based on the generated random field data, the finite element (FE) models of the soil-pipe system are established and the offshore spatial motions applied to pipelines are stochastically synthesized. Meanwhile, the impacts of soil spatial variability on the soil-pipe interaction and offshore motion propagation are investigated. Next, the probabilistic seismic demand models of FSSPs are derived via dynamic analyses and statistical regression, and the seismic fragility curves are generated. The influence of soil spatial variability on the seismic performance of FSSPs is examined by comparing the fragility curves between the random-field and random-variable cases. Finally, a fast assessment method for the ultimate bearing capacity is proposed to simply incorporate soil spatial variability in the seismic performance estimation of FSSPs. Numerical results highlight the necessity of incorporating soil spatial variability in seismic fragility analysis of FSSPs. The proposed assessment method can provide a great convenience for designers and engineers to obtain the accurate ultimate bearing capacity of FSSPs or other underground structures in the preliminary stage of seismic design.