Supersymmetric Chern–Simons theory in presence of a boundary in the light-like direction

Vohánka, Jiří; Faizal, Mir

doi:10.1016/j.nuclphysb.2015.12.010

Nuclear Physics B

2016

DOI: 10.1016/j.nuclphysb.2015.12.010

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Supersymmetric Chern–Simons theory in presence of a boundary in the light-like direction

Jiří Vohánka

Mir Faizal

Abstract: In this paper, we will analyze a three dimensional supersymmetric Chern-Simons theory on a manifold with a boundary. The boundary we will consider in this paper will be defined by n · x = 0, where n is a light-like vector. It will be demonstrated that this boundary is preserved under the action of the SIM (1) subgroup of the Lorentz group. Furthermore, the presence of this boundary will break half of the supersymmetry of the original theory. As the original Chern-Simons theory had N = 1 supersymmetry in absenc… Show more

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Cited by 13 publications

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“…The VSR provides a new mechanism for neutrino mass which conserves lepton number without introducing additional sterile states [20]. The Super-Yang-Mills theory in SIM(1) superspace and three dimensional Chern-Simons theory [21] are discussed in such schemes [22][23][24]. The superspace description of Lorentz violating p-form gauge theories is also presented [25].…”

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Lorentz-violating gaugeon formalism for rank-2 tensor theory

2019

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We develop a BRST symmetric gaugeon formalism for the Abelian rank-2 antisymmetric tensor field in the Lorentz breaking framework. The Lorentz breaking is achieved here by considering a proper subgroup of Lorentz group together with translation. In this scenario, the gaugeon fields together with the standard fields of the Abelian rank-2 antisymmetric tensor theory get mass. In order to develop the gaugeon formulation for this theory in VSR, we first introduce a set of dipole vector fields as a quantum gauge freedom to the action. In order to quantize the dipole vector fields, the VSR-modified gauge-fixing and corresponding ghost action are constructed as the classical action is invariant under a VSR-modified gauge transformation. Further, we present a Type I gaugeon formalism for the Abelian rank-2 antisymmetric tensor field theory in VSR. The gauge structures of Fock space constructed with the help of BRST charges are also discussed.

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Lorentz-violating gaugeon formalism for rank-2 tensor theory

2019

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Non-Abelian Gauge Theory in the Lorentz Violating Background

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Quantum gauge freedom in very special relativity

Upadhyay

Panigrahi

2017

Nuclear Physics B

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We demonstrate Yokoyama gaugeon formalism for the Abelian one-form gauge (Maxwell) as well as for Abelian two-form gauge theory in the very special relativity (VSR) framework. In VSR scenario, the extended action due to introduction of gaugeon fields also possesses form invariance under quantum gauge transformations. It is observed that the gaugeon field together with gauge field naturally acquire mass, which is different from the conventional Higgs mechanism. The quantum gauge transformation implements a shift in gauge parameter. Further, we analyse the BRST symmetric gaugeon formalism in VSR which embeds only one subsidiary condition rather than two. I. OVERVIEW AND MOTIVATIONIn recent times, the violations of Lorentz symmetry have been studied with great interest [1-6], though special relativity (SR), whose underlying Lorentz symmetry is valid at the largest energies available these days [7]. However, the violation of Lorentz symmetry has been considered as a possible evidence for Planck scale physics [8]. In this context, Cohen and Glashow [9] have proposed that the laws of physics need not be invariant under the full Lorentz group but rather under its subgroups that still preserves the basic elements of SR, like the constancy of the velocity of light. Any scheme whose spacetime symmetries consist of translations along with any Lorentz subgroups is referred to as very special relativity (VSR). Most common subgroups fulfilling the essential requirements are the homothety group HOM (2) (with three parameters) and the similitude group SIM (2) (with four parameters) [9]. The generators of HOM (2) are T 1 = K x + J y , T 2 = K y − J x , and K z , where J and K are the generators of rotations and boosts, respectively. The generators of SIM (2) are T 1 = K x + J y , T 2 = K y − J x , K z and J z . These subgroups will be enlarged to the full Lorentz group when supplemented with discrete spacetime symmetries CP . Recently, the three-dimensional supersymmetric Yang-Mills theory coupled to matter fields, (supersymmetric) Chern-Simons theory in SIM (1) superspace formalism [10] and SIM (2) superspace formalism [11] are derived. The Feynman rules and supergraphs [12] in SIM (2) superspace also has been studied.VSR admits natural origin to lepton-number conserving neutrino masses without the need for sterile (right-handed) states [13]. This implies that neutrinoless double beta decay is forbidden, if VSR is solely responsible for neutrino masses. Further, VSR is generalized to N = 1 SUSY gauge theories [14], where it is shown that these theories contain two conserved supercharges rather than the usual four. VSR is also modified by quantum corrections to produce a curved space-time with a cosmological constant [15], where it is shown that the symmetry group ISIM (2) does admit a 2-parameter family of continuous deformations, but none of these give rise to non-commutative translations analogous to those of the de-Sitter deformation of the Poincaré group. The VSR is generalized to curved space-times also, where it has been f...

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Supersymmetric Chern–Simons theory in presence of a boundary in the light-like direction

Cited by 13 publications

References 56 publications

Lorentz-violating gaugeon formalism for rank-2 tensor theory

Lorentz-violating gaugeon formalism for rank-2 tensor theory

Non-Abelian Gauge Theory in the Lorentz Violating Background

Quantum gauge freedom in very special relativity

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