1,720,981 research outputs found
Poisson gauge theory: a review
No full textIn this paper we overview the Poisson gauge theory focusing on the most recent developments. We discuss the general construction and its symplectic-geometric interpretation. We consider explicit realisations of the formalism for all non-commutativities of the Lie algebraic type. We discuss Seiberg-Witten maps between Poisson gauge field-theoretical models
How Many Surface Modes Does One See on the Boundary of a Dirac Material?
No full textWe present full expressions for the surface part of polarization tensor of a Dirac fermion confined in a half-space in 3+1 dimensions. We compare this tensor to the polarization tensor of eventual surface mode (which is a 2+1 dimensional Dirac fermion) and find essential differences in the conductivities in both Hall and normal sectors. Thus, the interaction with electromagnetic field near the boundary differs significantly in the full model and in the effective theory for the surface mode
Hamiltonian analysis in Lie-Poisson gauge theory
No full textLie-Poisson gauge formalism provides a semiclassical description of noncommutative U(1) gauge theory with Lie algebra type noncommutativity. Using the Dirac approach to constrained Hamiltonian systems, we focus on a class of Lie-Poisson gauge models, which exhibit an admissible Lagrangian description. The underlying noncommutativity is supposed to be purely spatial. Analyzing the constraints, we demonstrate that these models have as many physical degrees of freedom as there are present in the Maxwell theory
Four-dimensional noncommutative deformations of U(1) gauge theory and L∞ bootstrap
No full textWe construct a family of four-dimensional noncommutative deformations of U(1) gauge theory following a general scheme, recently proposed in JHEP 08 (2020) 041 for a class of coordinate-dependent noncommutative algebras. This class includes the su(2), the su(1, 1) and the angular (or λ-Minkowski) noncommutative structures. We find that the presence of a fourth, commutative coordinate x0 leads to substantial novelties in the expression for the deformed field strength with respect to the corresponding three-dimensional case. The constructed field theoretical models are Poisson gauge theories, which correspond to the semi-classical limit of fully noncommutative gauge theories. Our expressions for the deformed gauge transformations, the deformed field strength and the deformed classical action exhibit flat commutative limits and they are exact in the sense that all orders in the deformation parameter are present. We review the connection of the formalism with the L∞ bootstrap and with symplectic embeddings, and derive the L∞-algebra, which underlies our model
Remark on the synergy between the heat kernel techniques and the parity anomaly
No full textIn this paper, we demonstrate that not only the heat kernel techniques are useful for computation of the parity anomaly, but also the parity anomaly turns out to be a powerful mean in studying the heat kernel. We show that the gravitational parity anomaly on four-dimensional manifolds with boundaries can be calculated using the general structure of the heat kernel coefficient a5 for mixed boundary conditions, keeping all the weights of various geometric invariants as unknown numbers. The symmetry properties of the η-invariant allow to fix all the relevant unknowns. As a byproduct of this calculation, we get an efficient and independent crosscheck (and confirmation) of the correction of the general structure of a5 for mixed boundary conditions, previously suggested in [I. G. Moss, Anomalies, boundaries and the in-in formalism, J. Phys. A 45 (2012) 374022, https://doi.org/10.1088/1751-8113/45/37/374022]
Parity anomalies on 4D manifolds with boundaries
No full textWe discuss a parity breaking in theories of fermions, which are trapped inside four-manifolds with boundaries. Even though these theories are parity-invariant at the classical level, the radiative corrections induce parityviolating boundary terms. The effect is present in both gauge and gravitational sectors
The Gribov problem in noncommutative gauge theory
No full textfter reviewing Gribov ambiguity of non-Abelian gauge theories, a phenomenon relatedto the topology of the bundle of gauge connections, we show that there is a similar feature fornoncommutative QED over Moyal space, despite the structure group being Abelian, and weexhibit an infinite number of solutions for the equation of Gribov copies. This is a genuineeffect of noncommutative geometry which disappears when the noncommutative parametervanishes
κ-Minkowski-deformation of U(1) gauge theory
No full textWe construct a noncommutative kappa-Minkowski deformation of U(1) gauge theory, following a general approach, recently proposed in JHEP 08 (2020) 041. We obtain an exact (all orders in the non-commutativity parameter) expression for both the deformed gauge transformations and the deformed field strength, which is covariant under these transformations. The corresponding Yang-Mills Lagrangian is gauge covariant and reproduces the Maxwell Lagrangian in the commutative limit. Gauge invariance of the action functional requires a non-trivial integration measure which, in the commutative limit, does not reduce to the trivial one. We discuss the physical meaning of such a nontrivial commutative limit, relating it to a nontrivial space-time curvature of the undeformed theory. Moreover, we propose a rescaled kappa-Minkowski noncommutative structure, which exhibits a standard flat commutative limit
Parity anomaly in four dimensions
Full text linkIn an analogy to the odd-dimensional case we define the parity anomaly as the part of the one-loop effective action for fermions associated with spectral asymmetry of the Dirac operator. This quantity is computed directly on four-dimensional manifolds with a boundary and related to the Chern-Simons current on the boundary. Despite a quite unusual Chern-Simons level obtained, the action is gauge invariant and passes all consistency checks
Gravitational parity anomaly with and without boundaries
Full text linkAbstract
In this paper we consider gravitational parity anomaly in three and four dimensions. We start with a re-computation of this anomaly on a 3D manifold without boundaries and with a critical comparison of our results to the previous calculations. Then we compute the anomaly on 4D manifolds with boundaries with local bag boundary conditions. We find, that gravitational parity anomaly is localized on the boundary and contains a gravitational Chern-Simons terms together with a term depending of the extrinsic curvature. We also discuss the main properties of the anomaly, as the conformal invariance, relations between 3D and 4D anomalies, etc.</jats:p
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