BRST formulation of Chern-Simons gauge theory coupled to matter fields

In our recent paper, we systematized an inverse algorithm to obtain quiver gauge theory living on theM2-branes probing the singularities of a special kind of Calabi-Yau fourfold which were complex cones over toric Fanoℙ3,ℬ1,ℬ2,ℬ3. These quiver gauge theories cannot be given a dimer tiling presentation. We use the method of partial resolution to show that the toric data ofℂ4and Fanoℙ3can be embedded inside the toric data of Fanoℬtheories. This method indirectly justifies that the two-node quiver Chern-Simons theories corresponding toℂ4, Fanoℙ3, and their orbifolds can be obtained by higgsing matter fields of the three-node parent quiver corresponding to Fanoℬ1,ℬ2,ℬ3,ℬ4threefold.

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The Batalin–Vilkovisky formalism description of self-dual Chern–Simons gauge theory coupled to matter fields in superspace

International Journal of Modern Physics A ◽

10.1142/s0217751x20500207 ◽

2020 ◽

Vol 35 (05) ◽

pp. 2050020

Author(s):

Jialiang Dai

Keyword(s):

Gauge Theory ◽

Lagrangian Density ◽

Brst Symmetry ◽

Scalar Fields ◽

Covariant Form ◽

Brst Transformation ◽

Shift Symmetry ◽

Chern Simons ◽

Matter Fields

We construct the extended BRST and anti-BRST transformation by considering a shift symmetry both in Abelian and non-Abelian Chern–Simons theories coupled to scalar fields using the approach of Batalin–Vilkovisky quantization. The extended BRST invariant Lagrangian density is able to be addressed in the framework of superfield formalism with one fermionic coordinate. In the case of extended BRST–anti-BRST symmetry, it is shown that the Batalin–Vilkovisky action of the theory can be expressed in a covariant form with two fermionic coordinates in the superspace.

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DISCRETE AND CONTINUUM APPROACHES TO THREE-DIMENSIONAL QUANTUM GRAVITY

Modern Physics Letters A ◽

10.1142/s0217732391004140 ◽

1991 ◽

Vol 06 (39) ◽

pp. 3591-3600 ◽

Cited By ~ 40

Author(s):

HIROSI OOGURI ◽

NAOKI SASAKURA

Keyword(s):

Gauge Theory ◽

Moduli Space ◽

Three Dimensional ◽

Two Dimensional ◽

Analogue Model ◽

Gauge Invariant ◽

Invariant Functions ◽

Dimensional Lattice ◽

Chern Simons ◽

Dimensional Surface

It is shown that, in the three-dimensional lattice gravity defined by Ponzano and Regge, the space of physical states is isomorphic to the space of gauge-invariant functions on the moduli space of flat SU(2) connections over a two-dimensional surface, which gives physical states in the ISO(3) Chern–Simons gauge theory. To prove this, we employ the q-analogue of this model defined by Turaev and Viro as a regularization to sum over states. A recent work by Turaev suggests that the q-analogue model itself may be related to an Euclidean gravity with a cosmological constant proportional to 1/k2, where q=e2πi/(k+2).

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EQUIVALENCE OF TWO-DIMENSIONAL GRAVITIES

Modern Physics Letters A ◽

10.1142/s0217732390001414 ◽

1990 ◽

Vol 05 (16) ◽

pp. 1251-1258 ◽

Cited By ~ 4

Author(s):

NOUREDDINE MOHAMMEDI

Keyword(s):

Gauge Theory ◽

Explicit Solution ◽

Light Cone ◽

Equations Of Motion ◽

Two Dimensional ◽

Induced Gravity ◽

Light Cone Gauge ◽

Dimensional Gravity ◽

The Relationship ◽

Chern Simons

We find the relationship between the Jackiw-Teitelboim model of two-dimensional gravity and the SL (2, R) induced gravity. These are shown to be related to a two-dimensional gauge theory obtained by dimensionally reducing the Chern-Simons action of the 2+1 dimensional gravity. We present an explicit solution to the equations of motion of the auxiliary field of the Jackiw-Teitelboim model in the light-cone gauge. A renormalization of the cosmological constant is also given.

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REMARKS ON A CHERN–SIMONS-LIKE COUPLING

Modern Physics Letters A ◽

10.1142/s0217732311037121 ◽

2011 ◽

Vol 26 (37) ◽

pp. 2813-2821

Author(s):

PATRICIO GAETE

Keyword(s):

Gauge Theory ◽

Vector Field ◽

Static Potential ◽

Gauge Invariant ◽

Massive Vector ◽

Hidden Sector ◽

Dependent Variables ◽

Qualitative Nature ◽

Path Dependent ◽

Chern Simons

We consider the static quantum potential for a gauge theory which includes a light massive vector field interacting with the familiar U (1) QED photon via a Chern–Simons-like coupling, by using the gauge-invariant, but path-dependent, variables formalism. An exactly screening phase is then obtained, which displays a marked departure of a qualitative nature from massive axionic electrodynamics. The above static potential profile is similar to that encountered in axionic electrodynamics consisting of a massless axion-like field, as well as to that encountered in the coupling between the familiar U (1) QED photon and a second massive gauge field living in the so-called U (1)h hidden-sector, inside a superconducting box.

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THE PAULI TERM AS A GENERATOR OF FRACTIONAL SPIN

Modern Physics Letters A ◽

10.1142/s0217732311035912 ◽

2011 ◽

Vol 26 (19) ◽

pp. 1427-1432

Author(s):

J. S. N. FURTADO ◽

F. A. S. NOBRE

Keyword(s):

Fractional Statistics ◽

Fractional Spin ◽

Chern Simons ◽

Matter Fields

In this work, we show that contrary to what is commonly accepted by the community, the Chern–Simons term is not essential to fractional statistics. A Lagrangian whose dynamics is governed only by the Pauli term coupled to matter fields leads to the fractional spin. Despite its simplicity, development of this Lagrangian gives rise to essentially the same terms that appear in Chern–Simons models, such as those reported by Nobre and Almeida.13,8,9

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Nilpotent symmetries and Curci–Ferrari-type restrictions in 2D non-Abelian gauge theory: Superfield approach

International Journal of Modern Physics A ◽

10.1142/s0217751x17501937 ◽

2017 ◽

Vol 32 (33) ◽

pp. 1750193 ◽

Cited By ~ 1

Author(s):

N. Srinivas ◽

R. P. Malik

Keyword(s):

Gauge Theory ◽

The Self ◽

Abelian Gauge ◽

Abelian Gauge Theory ◽

Abelian Theory ◽

Matter Fields

We derive the off-shell nilpotent symmetries of the two [Formula: see text]-dimensional (2D) non-Abelian 1-form gauge theory by using the theoretical techniques of the geometrical superfield approach to Becchi–Rouet–Stora–Tyutin (BRST) formalism. For this purpose, we exploit the augmented version of superfield approach (AVSA) and derive theoretically useful nilpotent (anti-)BRST, (anti-)co-BRST symmetries and Curci–Ferrari (CF)-type restrictions for the self-interacting 2D non-Abelian 1-form gauge theory (where there is no interaction with matter fields). The derivation of the (anti-)co-BRST symmetries and all possible CF-type restrictions are completely novel results within the framework of AVSA to BRST formalism where the ordinary 2D non-Abelian theory is generalized onto an appropriately chosen [Formula: see text]-dimensional supermanifold. The latter is parametrized by the superspace coordinates [Formula: see text] where [Formula: see text] (with [Formula: see text]) are the bosonic coordinates and a pair of Grassmannian variables [Formula: see text] obey the relationships: [Formula: see text], [Formula: see text]. The topological nature of our 2D theory allows the existence of a tower of CF-type restrictions.

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