Bosonic Theory Research Articles

Bosonic quantum integrable systems and gauge theories

Bosonic quantum integrable systems and gauge theories

Time-reversal anomalies of QCD3 and QED3

Anomalies of global symmetry provide powerful tool to constrain the dynamics of quantum systems, such as anomaly matching in the renormalization group flow and obstruction to symmetric mass generation. In this note we compute the anomalies in 2+1d time-reversal symmetric gauge theories with massless fermions in the fundamental and rank-two tensor representations, where the gauge groups are SU(N), SO(N), Sp(N), U(1). The fermion parity is part of the gauge group and the theories are bosonic. The time-reversal symmetry satisfies T2 = 1 or T2 = M\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{M} $$\\end{document} where M\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{M} $$\\end{document} is an internal magnetic symmetry. We show that some of the bosonic gauge theories have time-reversal anomaly with c− ≠ 0 mod 8 that is absent in fermionic systems. The anomalies of the gauge theories can be nontrivial even when the number of Majorana fermions is a multiple of 16 and ν = 0.

On fusing matrices associated with conformal boundary conditions

In the context of rational conformal field theories (RCFT) we look at the fusing matrices that arise when a topological defect is attached to a conformal boundary condition. We call such junctions open topological defects. One type of fusing matrices arises when two open defects fuse while another arises when an open defect passes through a boundary operator. We use the topological field theory approach to RCFTs based on Frobenius algebra objects in modular tensor categories to describe the general structure associated with such matrices and how to compute them from a given Frobenius algebra object and its representation theory. We illustrate the computational process on the rational free boson theories. Applications to boundary renormalisation group flows are briefly discussed.

Entanglement entropy via double-cone regularization

This paper proposes an alternative regularization method for handling the ultraviolet behavior of entanglement entropy. Utilizing an iε prescription in the Euclidean double cone geometry, it accurately reproduces the universal behavior of entanglement entropy. The method is demonstrated in the free boson theory in arbitrary dimensions and two-dimensional conformal field theories. The findings highlight the effectiveness of the iε regularization method in addressing ultraviolet issues in quantum field theory and gravity, suggesting potential applications to other calculable quantities. Published by the American Physical Society 2024

Hydrodynamics, anomaly inflow and bosonic effective field theory

Euler hydrodynamics of perfect fluids can be viewed as an effective bosonic field theory. In cases when the underlying microscopic system involves Dirac fermions, the quantum anomalies should be properly described. In 1+1 dimensions the action formulation of hydrodynamics at zero temperature is reconsidered and shown to be equal to standard field-theory bosonization. Furthermore, it can be derived from a topological gauge theory in one extra dimension, which identifies the fluid variables through the anomaly inflow relations. Extending this framework to 3+1 dimensions yields an effective field theory/hydrodynamics model, capable of elucidating the mixed axial-vector and axial-gravitational anomalies of Dirac fermions. This formulation provides a platform for bosonization in higher dimensions. Moreover, the connection with 4+1 dimensional topological theories suggests some generalizations of fluid dynamics involving additional degrees of freedom.

Flows in the space of interacting chiral boson theories

We study interacting theories of N left-moving and N¯ right-moving Floreanini-Jackiw bosons in two dimensions. A parametrized family of such theories is shown to enjoy (nonmanifest) Lorentz invariance if and only if its Lagrangian obeys a flow equation driven by a function of the energy-momentum tensor. We discuss the canonical quantization of such theories along classical stress tensor flows, focusing on the case of the root-TT¯ deformation, where we obtain perturbative results for the deformed spectrum in a certain large-momentum limit. In the special case N=N¯, we consider the quantum effective action for the root-TT¯-deformed theory by expanding around a general classical background, and we find that the one-loop contribution vanishes for backgrounds with constant scalar gradients. Our analysis can also be interpreted via dual U(1) Chern-Simons theories in three dimensions, which might be used to describe deformations of charged AdS3 black holes or quantum Hall systems. Published by the American Physical Society 2024

Non-relativistic limits of bosonic and heterotic Double Field Theory

The known stringy non-relativistic (NR) limit of the universal NS-NS sector of supergravity has a finite Lagrangian due to non-trivial cancellations of divergent parts coming from the metric and the B-field. We demonstrate that in Double Field Theory (DFT) and generalised geometry these cancellations already happen at the level of the generalised metric, which is convergent in the limit c → ∞, implying that the NR limit can be imposed before solving the strong constraint. We present the c-expansion of the generalised metric, which reproduces the Non-Riemannian formulation of DFT at the (finite) leading order, and the c-expansion of the generalised frame, which contains divergences. We also extend this approach to the non-Abelian gauge field of Heterotic DFT assuming a convergent expansion for the O(D, D + n) generalised metric. From this proposal, we derive a novel c-expansion for the bosonic part of the heterotic supergravity which is, by construction, compatible with O(D, D)-symmetry.

Toward higher-spin symmetry breaking in the bulk

We present a new vacuum of the bosonic higher-spin gauge theory in d+1 dimensions, which has leftover symmetry of the Poincaré algebra in d dimensions. Its structure is very simple: the space-time geometry is that of anti–de Sitter space, while the only nonzero field is a scalar. The scalar extends along the Poincaré radial coordinate z and is shown to be linearly exact for an arbitrary mixture of its two Δ=2 and Δ=d−2 conformal branches. The obtained vacuum breaks the global higher-spin symmetry, leading to a broken phase that lives in the Minkowski space-time. Published by the American Physical Society 2024

The resurgence of the plateau in supersymmetric N\\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} = 1 Jackiw-Teitelboim gravity

Significant progresses have been made recently in understanding the spectral form factor of Jackiw-Teitelboim gravity, particularly at late times where non-perturbative effects are expected to play a dominant role. By focusing on a peculiar regime of large time and fixed temperature, called τ-scaling limit, it was found that it is possible to analytically investigate the late-time plateau directly through the gravitational genus expansion. We extend this analysis to the supersymmetric N\\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} = 1 generalization of the bosonic theory, revealing an interesting structure. First, we notice that in the τ-scaling limit the perturbative sum over genera truncates after a single term, which solely accounts for the ramp behaviour. Instead a non-perturbative completion, responsible for the plateau, is encoded into an exact formula coming from the properties of the chiral gaussian ensemble, governing the spectral properties of the supersymmetric theory. We are able to recover the non-perturbative contributions by slightly deforming the genus of the involved surfaces and using resurgence theory. We derive a closed-form analytical expression for the late-time plateau and a trans-series expansion that captures the ramp-plateau transition.

Unconstrained Lagrangian formulation for bosonic continuous spin theory in flat spacetime of arbitrary dimension

We have discovered two unconstrained forms of free Lagrangian for continuous spin(CS) theory in arbitrary flat spacetime dimension for bosonic case. These Lagrangians, unlike that by Schuster and Toro, do not include delta functions and are conventional. The first form consists of five kinds of totally symmetric helicity fields and one kind of gauge parameter. By introducing auxiliary creation and annihilation operators, each is combined into a state vector in Fock space, including all ranks one by one. The Lagrangian imposes no constraints, such as trace conditions, on these fields or the gauge parameter field. Additionally, the Lagrangian does not contain higher-order derivative terms. In the limit as CS parameter μ approaches zero, it naturally reproduces a Lagrangian for helicity fields in higher spin(HS) theory, known as unconstrained quartet formulation. Permitting third-order derivatives, we also obtain the second unconstrained form of Lagrangian that can be written in terms of three kinds of fields, including μ, similar to the formulation by Francia and Sagnotti. Partial gauge fixing and partial use of equations of motion (EOM) on this Lagrangian yield a Fronsdal-like Lagrangian with a single double-traceless field, including μ. By imposing further gauge fixing on the field in the EOM with respect to divergence and trace, we confirm the reproduction of the modified Wigner equations already known in literature.

Fermionic and Bosonic Partition Functions at Imaginary Chemical Potential as Bloch Functions

In this work it is pointed out that the phase transitions of the <i>d</i>+1 Gross-Neveu (fermionic) and <I>CP<SUP>N</SUP></I><sup>−1</sup> (bosonic) models at finite temperature and imaginary chemical potential can be mapped to transformations of Hubbard-like regular hexagonal to square lattice with the intermediate steps to be specific surfaces (irregular hexagonal kind) with an ordered construction based on the even indexed Bloch-Wigner-Ramakrishnan polylogarithm function. The zeros and extrema of the Clausen <i>Cl<sub>d</sub></i>(<i>θ</i>) function play an important role to the analysis since they allow us not only to study the fermionic and bosonic theories and their phase transitions but also the possibility to explore the existence of conductors arising from the correspondence between the partition functions of the two models and the Bloch and Wannier functions that play a crucial role in the tight-binding approximation in solid state physics. The main aim of this work is not only to unveil the relevance of the canonical partition functions of a fermionic and a bosonic model to Bloch states by using an imaginary chemical potential but also to examine the overlap between two Bloch wave-functions that differ by a lattice momentum that calculates the momentum transfer of a Bloch wave during the interaction with a lattice point of a hexagonal construction.

N\\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} = 2 supersymmetry in the twistor description of higher-spin holography

We study the holographic duality between higher-spin (HS) gravity in 4d and free vector models in 3d, with special attention to the role of N\\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} = 2 supersymmetry (SUSY). For the type-A bosonic bulk theory, dual to spin-0 fields on the boundary, there exists a twistor-space description; this maps both single-trace boundary operators and linearized bulk fields to spacetime-independent twistor functions, whose HS-algebra products compute all boundary correlators. Here, we extend this description to the type-B bosonic theory (dual to spin-1/2 fields on the boundary), and to the supersymmetric theory containing both. A key role is played by boundary bilocals, which in type-A are dual to the Didenko-Vasiliev 1/2-BPS “black hole”. We extend this to an infinite family of linearized 1/2-BPS “black hole” solutions. Remarkably, the full supersymmetric theory (along with the SUSY generators) fits in the same space of twistor functions as the type-A theory. Instead of two sets of bosonic bulk fields, the formalism sees one set of linearized fields, but with both types of boundary data allowed.

Bosonic rational conformal field theories in small genera, chiral fermionization, and symmetry/subalgebra duality

A (1 + 1)D unitary bosonic rational conformal field theory (RCFT) may be organized according to its genus, a tuple (c,C) consisting of its central charge c and a unitary modular tensor category C which describes the (2 + 1)D topological quantum field theory for which its maximally extended chiral algebra forms a holomorphic boundary condition. We establish a number of results pertaining to RCFTs in “small” genera, by which we informally mean genera with the central charge c and the number of primary operators rank(C) both not too large. We start by completely solving the modular bootstrap problem for theories with at most four primary operators. In particular, we characterize, and provide an algorithm which efficiently computes, the function spaces to which the partition function of any bosonic RCFT with rank(C)≤4 must belong. Using this result, and leveraging relationships between RCFTs and holomorphic vertex operator algebras which come from “gluing” and cosets, we rigorously enumerate all bosonic theories in 95 of the 105 genera (c,C) with c ≤ 24 and rank(C)≤4. This includes as (new) special cases the classification of chiral algebras with three primaries and c < 120/7 ∼ 17.14, and the classification of chiral algebras with four primaries and c < 62/3 ∼ 20.67. We then study two applications of our classification. First, by making use of chiral versions of bosonization and fermionization, we obtain the complete list of purely left-moving fermionic RCFTs with c < 23 as a corollary of the results of the previous paragraph. Second, using a (conjectural) concept which we call “symmetry/subalgebra duality,” we precisely relate our bosonic classification to the problem of determining certain generalized global symmetries of holomorphic vertex operator algebras.

Quantum Field Theory for Multipolar Composite Bosons with Mass Defect and Relativistic Corrections

Atomic high-precision measurements have become a competitive and essential technique for tests of fundamental physics, the Standard Model, and our theory of gravity. It is therefore self-evident that such measurements call for a consistent relativistic description of atoms that eventually originates from quantum field theories like quantum electrodynamics. Most quantum metrological approaches even postulate effective field-theoretical treatments to describe a precision enhancement through techniques like squeezing. However, a consistent derivation of interacting atomic quantum gases from an elementary quantum field theory that includes both the internal structure as well as the center of mass of atoms, has not yet been addressed. We present such a subspace effective field theory for interacting, spin carrying, and possibly charged ensembles of atoms composed of nucleus and electron that form composite bosons called cobosons, where the interaction with light is included in a multipolar description. Relativistic corrections to the energy of a single coboson, light-matter interaction, and the scattering potential between cobosons arise in a consistent and natural manner. In particular, we obtain a relativistic coupling between the coboson’s center-of-mass motion and internal structure encoded by the mass defect. We use these results to derive modified bound-state energies, including the motion of ions, modified scattering potentials, a relativistic extension of the Gross-Pitaevskii equation, and the mass defect applicable to atomic clocks or quantum clock interferometry. Published by the American Physical Society 2024

More on closed string effective actions at order α′2

Recent progress in string theory has unveiled the discovery of Neveu Schwarz-Neveu Schwarz couplings in bosonic and heterotic effective actions at order α′2, which were achieved by imposing O(1,1) symmetry on the circle reduction of classical effective actions. While the bosonic theory features 25 couplings, the heterotic theory encompasses 24 parity-even and 3 parity-odd couplings, excluding the pure gravity couplings. In this study, we redefine the even-parity couplings in the bosonic and heterotic theories through the application of appropriate field redefinitions, resulting in 10 and 8 couplings, respectively. To establish the validity of these couplings, a cosmological reduction is conducted, demonstrating that the cosmological couplings in the heterotic theory vanish, subject to one-dimensional field redefinitions that include the lapse function and total derivative terms. Additionally, it is observed that the cosmological couplings in the bosonic theory can be expressed as tr(S˙6). These results are consistent with existing literature, where such behavior is attributed to the pure gravity component of the couplings. Furthermore, the consistency of the obtained couplings with 4-point string theory S-matrix elements is confirmed. Published by the American Physical Society 2024

An exact method for bosonizing the Fermi surface in arbitrary dimensions

Inspired by the recent work by Delacretaz et. al. [Phys. Rev. Res. 4, 033131 (2022)], we rigorously derive an exact and simple method to bosonize a non-interacting fermionic system with a Fermi surface starting from a microscopic Hamiltonian. In the long-wavelength limit, we show that the derived bosonized action is exactly equivalent to the action obtained by Delacretaz et. al. In addition, we propose diagrammatic rules to evaluate correlation functions using our bosonized theory and demonstrate these rules by calculating the three- and four-point density correlation functions. We also consider a general density-density interaction and show that the simplest approximation in our bosonic theory is identical to RPA results.

When the moduli space is an orbifold: spontaneous breaking of continuous non-invertible symmetries

We investigate theories of Nambu-Goldstone bosons where the spontaneously broken continuous symmetry is non-invertible. In such theories, the vacua generically parameterize an orbifold. We study in detail the simplest example of a single free scalar with shift symmetry, modded by reflection symmetry. At singular points of the vacuum manifold, we show that the spectrum of NG excitations is reduced, in particular there are no single-particle states. At the smooth points, on the other hand, single NG modes are present. We show that this is a consequence of the fact that at those points one can construct invertible operators implementing the continuous symmetry on the Hilbert space.

Noncommutative field theory of the Tkachenko mode: Symmetries and decay rate

We construct an effective field theory describing the collective Tkachenko oscillation mode of a vortex lattice in a two-dimensional rotating Bose-Einstein condensate in the long-wavelength regime. The theory has the form of a noncommutative field theory of a Nambu-Goldstone boson, which exhibits a noncommutative version of dipole symmetry. From the effective field theory, we show that, at zero temperature, the decay width Γ of the Tkachenko mode scales with its energy E as Γ∼E3 in the low-energy limit. We also discuss the width of the Tkachenko mode at a small temperature. Published by the American Physical Society 2024

Dipole symmetries from the topology of the phase space and the constraints on the low-energy spectrum

We demonstrate the general existence of a local dipole conservation law in bosonic field theory. The scalar charge density arises from the symplectic form of the system, whereas the tensor current descends from its stress tensor. The algebra of spatial translations becomes centrally extended in presence of field configurations with a finite nonzero charge. Furthermore, when the symplectic form is closed but not exact, the system may, surprisingly, lack a well-defined momentum density. This leads to a theorem for the presence of additional light modes in the system whenever the short-distance physics is governed by a translationally invariant local field theory. We also illustrate this mechanism for axion electrodynamics as an example of a system with Nambu-Goldstone modes of higher-form symmetries.

Dynamics of quantum spin-nematics: Comparisons with canted antiferromagnets

The identification of spin-nematic states is challenging due to the absence of Bragg peaks. However, the study of dynamical physical quantities provides a promising avenue for characterizing these states. In this study, we investigate the dynamical properties of spin-nematic states in three-dimensional quantum spin systems in a magnetic field, using a two-component boson theory that incorporates magnons and bimagnons. Our particular focus lies on the dynamical spin structure factor at zero temperature and the nuclear magnetic resonance (NMR) relaxation rate at finite temperatures. Our findings reveal that the dynamical structure factor does not exhibit any diverging singularity across momentum and frequency while providing valuable information about the form factor of bimagnon states and the underlying structure of spin-nematic order. Furthermore, we find a temperature dependence in the NMR relaxation rate proportional to T3 at low temperatures, similar to canted antiferromagnets. A clear distinction arises as there is no critical divergence of the NMR relaxation rate at the spin-nematic transition temperature. Our theoretical framework provides a comprehensive understanding of the excitation spectrum and the dynamical properties of spin-nematic states, covering arbitrary spin values S and encompassing site and bond nematic orders. Additionally, we apply the same methodology to analyze these dynamical quantities in a canted antiferromagnetic state and compare the results with those in the spin-nematic states. Published by the American Physical Society 2024