Generalized Faddeev–Popov method for a deformed supersymmetric Yang–Mills theory

Weinreb, Paul H.; Faizal, Mir

doi:10.1016/j.physletb.2015.06.064

Cited by 16 publications

(1 citation statement)

References 48 publications

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“…In our earlier works [11][12][13][14][15][16][17], we have shown that any arbitrary Abelian p-form (p = 1, 2, 3) gauge theory in D = 2p dimensions of spacetime within the framework of BRST formalism and the N = 2 SUSY quantum mechanical models, turn out to be the tractable model for Hodge theory. It would be interesting to implement this idea in the case of a free particle system on a toric geometry [40], supersymmetric Yang-Mills [24,[41][42][43]. Furthermore, the derivation of proper (anti-)BRST symmetries with the help of superfield formalism would be a nice piece of work in the context of deformed super-Yang-Mills, supersymmetric Chern-Simons, ABJM and BLG theories [43][44][45].…”

Section: Off-shell Nilpotent (Anti-)brst Symmetry Transformations And...mentioning

confidence: 99%

Novel symmetries in Christ-Lee model

Kumar¹,

Shukla²

2016

EPL

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We demonstrate that the gauge-fixed Lagrangian of the Christ-Lee model respects four fermionic symmetries, namely; (anti-)BRST symmetries, (anti-)co-BRST symmetries within the framework of BRST formalism. The appropriate anticommutators amongst the fermionic symmetries lead to a unique bosonic symmetry. It turns out that the algebra obeyed by the symmetry transformations (and their corresponding conserved charges) is reminiscent of the algebra satisfied by the de Rham cohomological operators of differential geometry. We also provide the physical realizations of the cohomological operators in terms of the symmetry properties. Thus, the present model provides a simple model for the Hodge theory.

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Section: Off-shell Nilpotent (Anti-)brst Symmetry Transformations And...mentioning

confidence: 99%

Novel symmetries in Christ-Lee model

Kumar¹,

Shukla²

2016

EPL

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Super-Group Field Cosmology in Batalin-Vilkovisky Formulation

Upadhyay¹

2016

Int J Theor Phys

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In this paper, we study the third quantized super-group field cosmology, a model in multiverse scenario, in Batalin-Vilkovisky (BV) formulation. Further, we propose the superfield/super-antifield dependent BRST symmetry transformations. Within this formulation, we establish connection between the two different solutions of the quantum master equation within the BV formulation. I. INTRODUCTIONThe construction of a consistent theory of quantum gravity continues to be one of the major open problems in fundamental physics. Such a theory is very essential for the understanding of fundamental issues such as the origin of the Universe, the final evaporation of black holes, and the structure of space and time. Several approaches to quantum gravity have been developed, with a remarkable convergence [1]. The loop quantum gravity, a background-independent approach, is one of the powerful candidates quantizing gravity in mathematically rigorous and in non-perturbative way [2,3]. The development started with the introduction of Ashtekar-Barbero variables, the densitized triad and the Ashtekar connection [4-9]. However, Loop quantum cosmology is the result of applying principles of loop quantum gravity to cosmological settings. The ensuing framework of loop quantum cosmology was introduced by Martin Bojowald [10]. The mathematical structure of loop quantum cosmology is presented in Ref. [11]. Loop quantum cosmology is constructed via a truncation of the classical phase space of general relativity to spatially homogeneous situations, which is then quantized by using the methods and results of loop quantum gravity. The quantization of geometric operators are thereby transferred to the truncated models.However, the group field theories have been proposed as a kind of second quantization of canonical loop quantum gravity, in the sense that its canonical wave function turns into a dynamical (quantized) field [12,13]. The group field theories are basically described by the field theories on group manifolds (or their Lie algebras) which provide a background-independent third quantized formalism for gravity in any dimensions and signature [14,15]. In the group field theories, both the geometry and the topology are dynamical. The Feynman diagrams of such theories have an interpretation of the spacetimes and therefore the quantum amplitudes for these diagrams can be interpreted as algebraic realization of a path integral description of gravity [16,17].The topology changing processes can not be analyzed by second quantization approach. This brings group field theory into the conceptual framework of "third quantization", for a rather appealing idea [18][19][20][21][22][23][24][25]. The third quantization is a field theory on the space of geometries, rather than spacetime, which also allows for a dynamical description of topology change [26]. Remarkably, the third quantization of loop quantum gravity leads to the group field theory [27][28][29][30]. The Wheeler-De Witt (mini-superspace) approximations of the group field theory results in t...

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