Topological mass generation in non-Abelian gauge theory—geometric BRST quantization approach

We study the topological mass generation in the 4 dimensional non-Abelian gauge theory, which is the extension of Allen et al.’s work in the Abelian theory. It is crucial to introduce a one form auxiliary field in constructing the gauge invariant non-Abelian action which contains both the one form vector gauge field A and the two form antisymmetric tensor field B. As in the Abelian case, the topological coupling mB∧F, where F is the field strength of A, makes the transmutation among A and B possible, and consequently we see that the gauge field becomes massive. We find the BRST/anti-BRST transformation rule using the horizontality condition, and construct a BRST/anti-BRST invariant quantum action.

The Becchi–Rouet–Stora–Tyutin (BRST) quantization of a gauge theory in noncommutative geometry is carried out in the ‘‘matrix derivative’’ approach. BRST/anti-BRST transformation rules are obtained by applying the horizontality condition, in the superconnection formalism. A BRST/anti-BRST invariant quantum action is then constructed, using an adaptation of the method devised by Baulieu and Thierry-Mieg for the Yang–Mills case. The resulting quantum action turns out to be the same as that of a gauge theory in the ’t Hooft gauge with spontaneously broken symmetry. Our result shows that only the even part of the supergroup acts as a gauge symmetry, while the odd part effectively provides a global symmetry. We treat the general formalism first, then work out the SU(2/1) and SU(2/2) cases explicitly.

A dynamical non-Abelian two-form potential gives masses to vector bosons via a topological coupling.1 Unlike in the Abelian case, the two-form cannot be dualized to Goldstone bosons. Duality is restored by coupling a flat connection to the theory in a particular way, and the new action is then dualized to a nonlinear sigma model. The presence of the flat connection is crucial, which saves the original mechanism of Higgs-free topological mass generation from being dualized to a sigma model.

The 4-dimensional model with topological mass generation that has recently been presented by Dvali, Jackiw and Pi [G. Dvali, R. Jackiw, and S.-Y. Pi, Phys. Rev. Lett. 96, 081602 (2006), hep-th/0610228] is generalized to any even number of dimensions. As in the 4-dimensional model, the 2n-dimensional model describes a mass-generation phenomenon due to the presence of the chiral anomaly. In addition to this model, new 2n-dimensional models with topological mass generation are proposed, in which a Stueckelberg-type mass term plays a crucial role in the mass generation. The mass generation of a pseudoscalar field such as the eta-prime meson is discussed within this framework.

We construct all possible Weyl invariant actions in d=4 for linearized spin three field in a general gravitational background. The first action is obtained as the square of the generalized Weyl tensor for a spin three gauge field in nonlinear gravitational background. It is, however, not invariant under spin three gauge transformations. We then construct two other nontrivial Weyl but not gauge invariant actions which are linear in the Weyl tensor of the background geometry. We then discuss existence and uniqueness of a possible linear combination of these three actions which is gauge invariant. We do this at the linear order in the background curvature for Ricci flat backgrounds.

Motivated by application to multiple M5-branes, we study some properties of non-Abelian two-form gauge theories. We emphasize that the fake curvature condition which is commonly used in the literature would restrict the dynamics to be either a free theory or a topological system. We then propose a modification of transformation law which simplifies the gauge transformation of 3-form field strength and enables us to write down a gauge invariant action. We then argue that a generalization of Stueckelberg mechanism naturally gives mass to the two-form gauge field. For the application to multiple M5-branes, it should be identified with the KK modes.

A massive B∧F theory in (3+1) dimensions with a Kalb-Ramond field isdimensionally reduced, giving rise to two different topological terms, oneinvolving a scalar and a Kalb-Ramond field and another one equivalent tothe four-dimensional B∧F term. We constructed two actions with thesetopological terms and show that a topological mass generation mechanism canbe implemented. Using the non–Chern-Simons topological term, an action isproposed leading to a classical duality relation between Klein-Gordon andMaxwell actions. We also show that an action in (2+1) dimensions with theKalb-Ramond field is related by Buscher's duality transformation to amassive gauge-invariant Stükelberg-type theory.

We review the non-anticommutative Q-deformations of $$ \mathcal{N} $$ = (1, 1) supersymmetric theories in four-dimensional Euclidean harmonic superspace. These deformations preserve chirality and harmonic Grassmann analyticity. The associated field theories arise as a low-energy limit of string theory in specific backgrounds and generalize the Moyal-deformed supersymmetric field theories. A characteristic feature of the Q-deformed theories is the half-breaking of supersymmetry in the chiral sector of the Euclidean superspace. Our main focus is on the chiral singlet Q-deformation, which is distinguished by preserving the SO(4) ∼ Spin(4) “Lorentz” symmetry and the SU(2) R-symmetry. We present the superfield and component structures of the deformed $$ \mathcal{N} $$ = (1, 0) supersymmetric gauge theory as well as of hypermultiplets coupled to a gauge superfield: invariant actions, deformed transformation rules, and so on. We discuss quantum aspects of these models and prove their renormalizability in the Abelian case. For the charged hypermultiplet in an Abelian gauge superfield background we construct the deformed holomorphic effective action.

We review the non-Abelian tensor gauge field theory and analyze its free field equations for lower rank gauge fields when the interaction coupling constant tends to zero. The free field equations are written in terms of the first-order derivatives of extended field strength tensors similar to the electrodynamics and non-Abelian gauge theories. We determine the particle content of the free field equations and count the propagating modes which they describe. In four-dimensional spacetime the rank-2 gauge field describes propagating modes of helicity two and zero. We show that the rank-3 gauge field describes propagating modes of helicity-three and a doublet of helicity-one gauge bosons. Only four-dimensional spacetime is physically acceptable, because in five- and higher-dimensional spacetime the equation has solutions with negative norm states. We discuss the structure of the particle spectrum for higher rank gauge fields.

In this review we present the salient features of dynamical chaos in classical gauge theories with spatially homogeneous fields. The chaotic behaviour displayed by both abelian and non-abelian gauge theories and the effect of the Higgs term in both cases are discussed. The role of the Chern-Simons term in these theories is examined in detail. Whereas, in the abelian case, the pure Chern-Simons-Higgs system is integrable, addition of the Maxwell term renders the system chaotic. In contrast, the non-abelian Chern-Simons-Higgs system is chaotic both in the presence and the absence of the Yang-Mills term. We support our conclusions with numerical studies on plots of phase trajectories and Lyapunov exponents. Analytical tests of integrability such as the Painleve criterion are carried out for these theories. The role of the various terms in the Hamiltonians for the abelian Higgs, Yang-Mills-Higgs and Yang-Mills-Chern-Simons-Higgs systems with spatially homogeneous fields, in determining the nature of order-disorder transitions is highlighted, and the effects are shown to be counter-intuitive in the last-named system.

Hartle's generalized quantum mechanics in the sum-over-histories formalism is used to describe a non-Abelian gauge theory. Predictions are made for certain alternatives, with particular attention given to coarse grainings involving the constraint. In this way, the theory is compared to other quantum-mechanical descriptions of gauge theories in which the constraints are imposed by hand. The vanishing of the momentum space constraint is seen to hold, both through a simple formal argument and via a more careful description of the Lorentzian path integral as defined on a spacetime lattice. The configuration space realization of the constraint is shown to behave in a more complicated fashion. For some coarse grainings, we recover the known result from an Abelian theory, that coarse grainings by values of the constraint either predict its vanishing or fail to decohere. However, sets of alternatives defined in terms of a more complicated quantity in the Abelian case are exhibited where definite predictions can be made which disagree with the assumption that the constraints vanish. Finally, the configuration space sum-over-histories theory is exhibited in a manifestly Lorentz-invariant formulation.

An inflationary scenario is expected to be embedded into an ultraviolet (UV) complete theory such as string theory. The effect of UV complete theories may appear as nontrivial kinetic terms in the low energy effective field theory, which provides a nontrivial geometry in field space. In this paper, we study the effect of the geometry of multi-form-field space on an inflationary scenario. In particular, we focus on the geometric destabilization mechanism which induces the phase transition from the conventional slow-roll inflation to a novel inflationary scenario. Anisotropic inflation is a typical example of the new phase. To conform to observations, we restrict us to isotropic configuration of form fields. We clarify the conditions for the onset of the destabilization and reveal the geometric structure of attractors after the destabilization. We classify the viable models from the observational point of view. We also investigate the features of the primordial fluctuations and find the similarity to hyperbolic inflation. By calculating the power spectrum, we make several phenomenological predictions which are useful to discriminate our models from others inflation models. We found the scalar-to-tensor r will be suppressed by large one-form gauge fields, while it has the same order as the slow roll parameter r ∼ \U0001d4aa(1)ϵ for large two-from gauge fields.

We present a dual formulation of the Cosserat theory of elasticity. In this theory a local element of an elastic body is described in terms of local displacement and local orientation. Upon the duality transformation these degrees of freedom map onto a coupled theory of a U(1) vector-valued one-form gauge field and an ordinary U(1) gauge field. We discuss the degrees of freedom in the corresponding gauge theories, relation to symmetric tensor gauge theories, the defect matter and coupling to the curved space.

Non-Abelian gauge theories underlie our understanding of fundamental forces in nature, and developing tailored quantum hardware and algorithms to simulate them is an outstanding challenge in the rapidly evolving field of quantum simulation. Here we take an approach where gauge fields, discretized in spacetime, are represented by qudits and are time evolved in Trotter steps with multiqudit quantum gates. This maps naturally and hardware efficiently to an architecture based on Rydberg tweezer arrays, where long-lived internal atomic states represent qudits, and the required quantum gates are performed as holonomic operations supported by a Rydberg blockade mechanism. We illustrate our proposal for a minimal digitization of SU(2) gauge fields, demonstrating a significant reduction in circuit depth and gate errors in comparison to a traditional qubit-based approach, which puts simulations of non-Abelian gauge theories within reach of NISQ devices.

Dimension two gluon condensates in a variety of gauges and a gauge invariant Yang-Mills action with a mass