Wess-Zumino Term Research Articles

Geometric BV for twisted Courant sigma models and the BRST power finesse

We study twisted Courant sigma models, a class of topological field theories arising from the coupling of 3D 0-/2-form BF theory and Chern-Simons theory and containing a 4-form Wess-Zumino term. They are examples of theories featuring a nonlinearly open gauge algebra, where products of field equations appear in the commutator of gauge transformations, and they are reducible gauge systems. We determine the solution to the master equation using a technique, the BRST power finesse, that combines aspects of the AKSZ construction (which applies to the untwisted model) and the general BV-BRST formalism. This allows for a geometric interpretation of the BV coefficients in the interaction terms of the master action in terms of an induced generalised connection on a 4-form twisted (pre-)Courant algebroid, its Gualtieri torsion and the basic curvature tensor. It also produces a frame independent formulation of the model. We show, moreover, that the gauge fixed action is the sum of the classical one and a BRST commutator, as expected from a Schwarz type topological field theory.

A basic examination of the gauged model of the Floreanini-Jackiw chiral boson within the framework of BRST symmetry

We consider the gauged model of Floreanini-Jackiw chiral boson which is generated from the chiral boson with parameter-free Faddeevian anomaly. This model does not have a manifestly Lorentz co-variant structure. However, it is exactly solvable and has a physical subspace that is precisely Lorentz invariant. The recommendation of Mitra and Rajaraman makes this model gauge invariant in the usual phasespace. Additionally, Wess-Zumino terms for this model are constructed to make it gauge-invariant which allows BRST embedding of the resulting gauge-invariant theory. Despite the strange structural appearance of the models when viewed in terms of Lorentz covariance BRST invariant reformulation has been found possible. Additionally, it has been observed that being supplemented with BRST symmetry, anti-BRST symmetry plays a crucial role in pinpointing the specific symmetric physical states.

Dualities of 3D \U0001d4a9 = 1 SQCD from Branes and non-SUSY deformations

We study the dynamics of an ‘electric’ \U0001d4a9 = 1 3D textrm{U}{left({N}_cright)}_{k,k+frac{N_c}{2}} SQCD theory. By embedding the theory in string theory, we propose that the theory admits a ‘magnetic’ dual and analyse the low energy dynamics of the theory using its dual. When frac{N_f}{2}ge frac{N_c}{2}-k the IR dynamics is described by either a TQFT for large quark masses, or a Grassmannian and a Wess-Zumino (WZ) term for small masses. We also consider non-supersymmetric mass deformations and RG flows in the vicinity of the SUSY point and find agreement between the IR of the electric and its magnetic dual. When frac{N_f}{2}<frac{N_c}{2}-k supersymmetry is broken and the IR dynamics is a described by a TQFT accompanied by a Goldstino. We also discuss SQCD theories based on SO/USp gauge groups.

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.

Gauge symmetry of the chiral Schwinger model from an improved gauge unfixing formalism

In this paper, the Hamiltonian structure of the bosonized chiral Schwinger model (BCSM) is analyzed. From the consistency condition of the constraints obtained from the Dirac method, we can observe that this model presents, for certain values of the α parameter, two second-class constraints, which means that this system does not possess gauge invariance. However, we know that it is possible to disclose gauge symmetries in such a system by converting the original second-class system into a first-class one. This procedure can be done through the gauge unfixing (GU) formalism by acting with a projection operator directly on the original second-class Hamiltonian, without adding any extra degrees of freedom in the phase space. One of the constraints becomes the gauge symmetry generator of the theory and the other one is disregarded. At the end, we have a first-class Hamiltonian satisfying a first-class algebra. Here, our goal is to apply a new scheme of embedding second-class constrained systems based on the GU formalism, named improved GU formalism, in the BCSM. The original second-class variables are directly converted into gauge invariant variables, called GU variables. We have verified that the Poisson brackets involving the GU variables are equal to the Dirac brackets between the original second-class variables. Finally, we have found that our improved GU variables coincide with those obtained from an improved BFT method after a particular choice for the Wess-Zumino terms.

Exact WKB analysis for SUSY and quantum deformed potentials: Quantum mechanics with Grassmann fields and Wess-Zumino terms

Quantum deformed potentials arise naturally in quantum mechanical systems of one bosonic coordinate coupled to ${N}_{f}$ Grassmann valued fermionic coordinates, or to a topological Wess-Zumino term. These systems decompose into sectors with a classical potential plus a quantum deformation. Using exact Wentzel-Kramers-Brillouin, we derive exact quantization condition and its median resummation. The solution of median resummed form gives physical Borel-Ecalle resummed results, as we show explicitly in quantum deformed double- and triple-well potentials. Despite the fact that instantons have finite actions, for generic quantum deformation, they do not contribute to the energy spectrum at leading order in semiclassics. For certain quantized quantum deformations, where the alignment of levels to all order in perturbation theory occurs, instantons contribute to the spectrum. If deformation parameter is not properly quantized, their effect disappears, but higher-order effects in semiclassics survive. In this sense, we classify saddle contributions as fading and robust. Finally, for quantum deformed triple-well potential, we demonstrate the perturbative/nonperturbative relation, by computing period integrals and Mellin transform.

Super AKSZ construction, integral forms, and the 2-dimensional mathcal{N} = (1, 1) sigma model

We discuss a natural extension of the AKSZ construction to the case where the source is given by a supermanifold with a chosen integral form. We then focus on the special case with the target given by a Courant algebroid. In the simplest case this leads to the BV version of the super Chern-Simons theory, as developed by Grassi-Maccaferri and Cremonini-Grassi. In the case of exact Courant algebroids we derive the 2-dimensional mathcal{N} = (1, 1) sigma model on the boundary, together with the Wess-Zumino term, paralleling the approach of Ševera in the bosonic case.

The BV action of 3D twisted R-Poisson sigma models

We determine the solution to the classical master equation for a 3D topological field theory with Wess-Zumino term and an underlying geometrical structure of a twisted R-Poisson manifold on its target space. The graded geometry of the target space departs from the usual QP structure encountered in the AKSZ construction of topological sigma models, the obstruction being attributed to the presence of the Wess-Zumino 4-form. Due to the inapplicability of the AKSZ construction in this case, we set up the traditional BV/BRST formalism for twisted R-Poisson sigma models in any dimension, which feature an open gauge algebra and constitute multiple stages reducible constrained Hamiltonian systems. An unusual feature of the theories is that they exhibit non-linear openness of the gauge algebra, in other words products of the equations of motion appear in them. Nevertheless, we find the BV action in presence of the 4-form twist in 3D, namely for a specific 4-form twisted (pre-)Courant sigma model. Moreover, we provide a complete set of explicit formulas for the off-shell nilpotent BV operator for untwisted R-Poisson sigma models in any dimension.

Homotopy momentum sections on multisymplectic manifolds

We introduce a notion of a homotopy momentum section on a Lie algebroid over a pre-multisymplectic manifold. A homotopy momentum section is a generalization of the momentum map with a Lie group action and the momentum section on a pre-symplectic manifold, and is also a generalization of the homotopy momentum map on a multisymplectic manifold. We show that a gauged nonlinear sigma model with Wess-Zumino term with Lie algebroid gauging has the homotopy momentum section structure.

Light vectors coupled to anomalous currents with harmless Wess-Zumino terms

We reconsider the case of light vectors coupled to anomalous fermionic currents, focusing on the interplay between ultraviolet and infrared dynamics. Taking as a general framework the gauging of the Standard Model accidental symmetries, we show that it is possible to devise an anomaly-free ultraviolet completion with mostly chiral heavy fermions such that anomalous Wess-Zumino terms are suppressed in the infrared, thus relaxing would-be strong bounds from the longitudinal emission of light vectors coupled to nonconserved currents. We classify such scenarios and show that they will be extensively probed at the high-luminosity phase of the LHC via the measurement of the $h\ensuremath{\rightarrow}Z\ensuremath{\gamma}$ rate and the direct search for nondecoupling charged leptons.

Mapping Topology of Skyrmions and Fractional Quantum Hall Droplets to Nuclear EFT for Ultra-Dense Baryonic Matter

We describe the mapping at high density of topological structure of baryonic matter to a nuclear effective field theory that implements hidden symmetries emergent from strong nuclear correlations. The theory constructed is found to be consistent with no conflicts with the presently available observations in both normal nuclear matter and compact-star matter. The hidden symmetries involved are “local flavor symmetry” of the vector mesons identified to be (Seiberg-)dual to the gluons of QCD and hidden “quantum scale symmetry” with an IR fixed point with a “genuine dilaton (GD)” characterized by non-vanishing pion and dilaton decay constants. Both the skyrmion topology for Nf≥2 baryons and the fractional quantum Hall (FQH) droplet topology for Nf=1 baryons are unified in the “homogeneous/hidden” Wess–Zumino term in the hidden local symmetry (HLS) Lagrangian. The possible indispensable role of the FQH droplets in going beyond the density regime of compact stars approaching scale-chiral restoration is explored by moving toward the limit where both the dilaton and the pion go massless.

Effective field theories for gapless phases with fractons via a coset construction

Fractons are particles with restricted mobility. We give a symmetry-based derivation of effective field theories of gapless phases with fractonic topological defects, such as solids and supersolids, using a coset construction. The resulting theory is identified as the Cosserat elasticity theory, which reproduces the conventional symmetric elasticity theory at low energies. The construction can be viewed as a dynamical realization of the inverse Higgs mechanism. We incorporate topological defects such as dislocations and disclinations, which are nontrivially related by the Bianchi identities of defect gauge fields. The origin of the fractonic nature of defects in those systems can be traced back to the semidirect product structure of translational and rotational groups. The construction is immediately extendable to higher dimensions and systems with broken translational symmetries, such as solids, supersolids, and vortex crystals. We identify Wess-Zumino terms in supersolids, which induce quasiparticle scatterings on topological defects.

Sigma-model analysis of SU(3) antiferromagnetic spins on the triangular lattice

Using field-theoretic techniques, we study the $\mathrm{SU}(3)$ analog of antiferromagnetic Heisenberg spin model on the triangular lattice putting the $p$-box symmetric representation on each site. Taking the large-$p$ limit, we show that the low-energy effective theory is described by a $(2+1)$-dimensional relativistic $\mathrm{SU}(3)/\mathrm{U}{(1)}^{2}$ nonlinear sigma model. Since the target space has a nontrivial homotopy ${\ensuremath{\pi}}_{2}(\mathrm{SU}(3)/\mathrm{U}{(1)}^{2})\ensuremath{\simeq}{\mathbb{Z}}^{2}$, this model has two kinds of magnetic skyrmions, which can be created and annihilated by monopole instantons. By careful analysis of the Wess-Zumino term in the spin coherent path integral, we compute the Berry phase for these monopoles and it produces the destructive interference. This restricts possible perturbations of the effective Lagrangian by monopole operators, and we see that the valence-bond-solid (VBS) phase should have degenerate ground states when $p\ensuremath{\notin}3\mathbb{Z}$. We also compute 't Hooft anomalies to constrain possible phases of this system, and a direct phase transition between N\'eel and VBS phases is supported from the anomaly matching.

Topological field theories induced by twisted R-Poisson structure in any dimension

We construct a class of topological field theories with Wess-Zumino term in spacetime dimensions ≥ 2 whose target space has a geometrical structure that suitably generalizes Poisson or twisted Poisson manifolds. Assuming a field content comprising a set of scalar fields accompanied by gauge fields of degree (1, p − 1, p) we determine a generic Wess-Zumino topological field theory in p + 1 dimensions with background data consisting of a Poisson 2-vector, a (p + 1)-vector R and a (p + 2)-form H satisfying a specific geometrical condition that defines a H-twisted R-Poisson structure of order p + 1. For this class of theories we demonstrate how a target space covariant formulation can be found by means of an auxiliary connection without torsion. Furthermore, we study admissible deformations of the generic class in special spacetime dimensions and find that they exist in dimensions 2, 3 and 4. The two-dimensional deformed field theory includes the twisted Poisson sigma model, whereas in three dimensions we find a more general structure that we call bi-twisted R-Poisson. This extends the twisted R-Poisson structure of order 3 by a non-closed 3-form and gives rise to a topological field theory whose covariant formulation requires a connection with torsion and includes a twisted Poisson sigma model in three dimensions as a special case. The relation of the corresponding structures to differential graded Q-manifolds based on the degree shifted cotangent bundle T*[p]T*[1]M is discussed, as well as the obstruction to them being QP-manifolds due to the Wess-Zumino term.

BRST and Superfield Formalism—A Review

This article, which is a review with substantial original material, is meant to offer a comprehensive description of the superfield representations of BRST and anti-BRST algebras and their applications to some field-theoretic topics. After a review of the superfield formalism for gauge theories, we present the same formalism for gerbes and diffeomorphism invariant theories. The application to diffeomorphisms leads, in particular, to a horizontal Riemannian geometry in the superspace. We then illustrate the application to the description of consistent gauge anomalies and Wess–Zumino terms for which the formalism seems to be particularly tailor-made. The next subject covered is the higher spin YM-like theories and their anomalies. Finally, we show that the BRST superfield formalism applies as well to the N=1 super-YM theories formulated in the supersymmetric superspace, for the two formalisms go along with each other very well.

Vector dominance, one flavored baryons, and QCD domain walls from the "hidden" Wess-Zumino term

We further explore a recent proposal that the vector mesons in QCD have a special role as Chern-Simons fields on various QCD objects such as domain walls and the one flavored baryons. We compute contributions to domain wall theories and to the baryon current coming from a generalized Wess-Zumino term including vector mesons. The conditions that lead to the expected Chern-Simons terms and the correct spectrum of baryons, coincide with the conditions for vector meson dominance. This observation provides a theoretical explanation to the phenomenological principle of vector dominance, as well as an experimental evidence for the identification of vector mesons as the Chern-Simons fields. By deriving the Chern-Simons theories directly from an action, we obtain new results about QCD domain walls. One conclusion is the existence of a first order phase transition between domain walls as a function of the quarks' masses. We also discuss applications of our results to Seiberg duality between gluons and vector mesons and provide new evidence supporting the duality.

A non-relativistic limit of NS-NS gravity

We discuss a particular non-relativistic limit of NS-NS gravity that can be taken at the level of the action and equations of motion, without imposing any geometric constraints by hand. This relies on the fact that terms that diverge in the limit and that come from the Vielbein in the Einstein-Hilbert term and from the kinetic term of the Kalb-Ramond two-form field cancel against each other. This cancelling of divergences is the target space analogue of a similar cancellation that takes place at the level of the string sigma model between the Vielbein in the kinetic term and the Kalb-Ramond field in the Wess-Zumino term. The limit of the equations of motion leads to one equation more than the limit of the action, due to the emergence of a local target space scale invariance in the limit. Some of the equations of motion can be solved by scale invariant geometric constraints. These constraints define a so-called Dilatation invariant String Newton-Cartan geometry.

Comments on gauge anomalies at dimension-six in the Standard Model Effective Field Theory

We study whether higher-dimensional operators in effective field theories, in particular in the Standard Model Effective Field Theory (SMEFT), can source gauge anomalies via the modification of the interactions involved in triangle diagrams. We find no evidence of such gauge anomalies at the level of dimension-6 operators that can therefore be chosen independently to each others without spoiling the consistency of SMEFT, at variance with recent claims. The underlying reason is that gauge-invariant combinations of Goldstone bosons and massive gauge fields are allowed to couple to matter currents which are not conserved. We show this in a toy model by computing the relevant triangle diagrams, as well as by working out Wess-Zumino terms in the bosonic EFT below all fermion masses. The same approach applies directly to the Standard Model both at the renormalisable level, providing a convenient and unusual way to check that the SM is anomaly free, as well as at the non-renormalisable level in SMEFT.

Stable and unstable Dp-branes in p-brane Newton–Cartan background

We formulate Dp-brane Newton–Cartan (NC) background through the limiting procedure from relativistic Dirac–Born–Infeld action and Wess–Zumino term. We also determine action for unstable D(p + 1)-brane in Dp-brane NC background and study its properties.

Classification of dark solitons via topological vector potentials.

Dark solitons are some of the most interesting nonlinear excitations and are considered to be the one-dimensional topological analogs of vortices. However, in contrast to their two-dimensional vortex counterparts, the topological characteristics of a dark soliton are far from fully understood because the topological charge defined according to the phase jump cannot reflect its essential property. Here, similar to the complex extension used in the exploration of the partition-function zeros to depict thermodynamic states, we extend the complex coordinate space to explore the density zeros of dark solitons. Surprisingly we find that these zeros constitute some pointlike magnetic fields, each of which has a quantized magnetic flux of elementary π. The corresponding vector potential fields demonstrate the topology of the Wess-Zumino term and can depict the essential characteristics of dark solitons. Then we classify the dark solitons according to the Euler characteristic of the topological manifold of the vector potential fields. Our study not only reveals the topological features of dark solitons but can also be applied to explore and identify new dark solitons with high topological complexity.