In this letter, we will study the Chern-Simons-matter theory in Harmonic
superspace. It will be shown that this superspace is well suited to write
theories with high amount of supersymmetry. This will be done using harmonic
variables. The harmonic superspace will have N=3 supersymmetry. It will be argued that it will
be possible to analyse this theory in non-anticommutative superspace. The
non-anticommutative superspace for this theory will be explicitly constructed.
Cite this paper
Sofi, A. H. and Majeed, S. U. (2015). Chern-Simons-Matter Theory in Superspace Formalism. Open Access Library Journal, 2, e1421. doi: http://dx.doi.org/10.4236/oalib.1101421.
Galperin,
A., Ivanov, E., Kalitzin, S., Ogievetsky, V. and Sokatchev, E. (1984) Unconstrained N = 2 Matter, Yang-Mills and Supergravity Theories in Harmonic Superspace. Classical and Quantum Gravity, 1, 469. http://dx.doi.org/10.1088/0264-9381/1/5/004
Soloviev, M.A. (2013) Algebras with
Convergent Star Products and Their Representations in Hilbert Spaces. Journal of Mathematical Physics, 54, Article
ID: 073517. http://dx.doi.org/10.1063/1.4815996
You, Y. and Fradkin, E. (2013) Field Theory
of Nematicity in the Spontaneous Quantum Anomalous Hall Effect. Physical
Review B, 88, Article ID: 235124. http://dx.doi.org/10.1103/PhysRevB.88.235124
Piatek, M. (2014) Classical Torus Conformal Block, N = 2* Twisted
Super-Potential and the Accessory Parameter of Lamé Equation. Journal
of High Energy Physics, 2014, 124. http://dx.doi.org/10.1007/JHEP03(2014)124
Papenbrock, T. and Weidenmüller, H.A. (2014)
Effective Field Theory for Finite Systems with Spontaneously Broken Symmetry. Physical Review C, 89, Article ID: 014334. http://dx.doi.org/10.1103/PhysRevC.89.014334
Ali,
A.F., Faizal, M. and Majumder, B. (2015) Absence of an Effective Horizon for Black Holes in Gravity’s
Rainbow. EPL (Europhysics Letters), 109, Article ID: 20001. http://dx.doi.org/10.1209/0295-5075/109/20001
Faizal, M. and
Khan, M. (2011) A Superspace Formulation of the BV Action for Higher Derivative
Theories. The European Physical Journal
C-Particles and Fields, 71, 1-5. http://dx.doi.org/10.1140/epjc/s10052-011-1603-8
Faizal, M. (2014) Deformation of the Wheeler-DeWitt
Equation. International Journal of Modern
Physics A, 29, Article ID: 1450106. http://dx.doi.org/10.1142/S0217751X14501061
Faizal, M. (2014) Consequences of
Deformation of the Heisenberg Algebra. International Journal of Geometric Methods in Modern Physics, 12, Article ID: 1550022.
Witten, E. (2004) Perturbative Gauge Theory
as a String Theory in Twistor Space. Communications in Mathematical Physics, 252, 189-258. http://dx.doi.org/10.1007/s00220-004-1187-3
Seiberg, N. (2003) Noncommutative Superspace,
Script N =
1/2 Supersymmetry, Field Theory and String Theory. Journal of High Energy Physics, 2003,
010. http://dx.doi.org/10.1088/1126-6708/2003/06/010
Faizal, M. (2011) Spontaneous Breaking of
Lorentz Symmetry by Ghost Condensation in Perturbative Quantum Gravity. Journal of Physics A: Mathematical and Theoretical, 44, Article ID: 402001. http://dx.doi.org/10.1088/1751-8113/44/40/402001
Cachazo, F., Seiberg, N. and Witten, E.
(2003) Chiral Rings and Phases of Supersymmetric Gauge Theories. Journal of High Energy Physics, 2003,
018. http://dx.doi.org/10.1088/1126-6708/2003/04/018
Faizal, M. (2012) Multiverse in the Third
Quantized Horava-Lifshitz Theory of Gravity. Modern Physics Letters A, 27, Article ID: 1250007. http://dx.doi.org/10.1142/S0217732312500071
Witten, E. (2003) Chiral Ring of Sp(N) and
SO(N) Supersymmetric Gauge Theory in Four Dimensions. Chinese Annals
of Mathematics, 24,
403. http://dx.doi.org/10.1142/S0252959903000402
Faizal, M. and Smith, D.J.
(2012) Supersymmetric Chern-Simons Theory in the Presence of a Boundary. Physical Review D, 85, Article ID:
105007. http://dx.doi.org/10.1103/PhysRevD.85.105007
Faizal, M. (2012) Noncommutativity and
Non-Anticommutativity Perturbative Quantum Gravity. Modern Physics Letters A, 27, Article ID: 1250075. http://dx.doi.org/10.1142/S0217732312500757
Friedmann, T. and Witten, E. (2003) Unification Scale, Proton Decay, and Manifolds of G2 Holonomy. Advances in Theoretical and Mathematical
Physics, 7, 577-617. http://dx.doi.org/10.4310/ATMP.2003.v7.n4.a1
Faizal,
M. (2012) Gauge and Supersymmetric Invariance of a Boundary Bagger-Lambert-Gustavsson
Theory. Journal of High Energy Physics,
2012, 17. http://dx.doi.org/10.1007/JHEP04(2012)017
Faizal, M. (2012) The BV Formalization of
Chern-Simons
Theory on Deformed Superspace. Communications
in Theoretical Physics, 58, 704. http://dx.doi.org/10.1088/0253-6102/58/5/14
Faizal, M. (2014) Absence of Black Holes
Information Paradox in Group Field Cosmology. International Journal of Geometric Methods in Modern Physics, 11, Article ID: 1450010. http://dx.doi.org/10.1142/S0219887814500108
Nazaryan, V. and Carlson, C.E. (2005) Field
Theory in Noncommutative Minkowski Superspace. Physical Review D, 71, Article ID: 025019. http://dx.doi.org/10.1103/PhysRevD.71.025019
Nazaryan, V. and Carlson, C.E. (2005) A Field
Theoretical Model in Noncommutative Minkowski Superspace. International Journal of Modern Physics A, 20, 3495-3501. http://dx.doi.org/10.1142/S0217751X05026820
Faizal, M. (2013) Deformed Super-Yang-Mills
in Batalin-Vilkovisky Formalism. International
Journal of Theoretical Physics, 52, 392-403. http://dx.doi.org/10.1007/s10773-012-1344-y
Kobayashi, Y. and Sasaki, S. (2005) Nonlocal
Wess-Zumino Model on Nilpotent Noncommutative Superspace. Physical Review D, 72, Article ID: 065015. http://dx.doi.org/10.1103/PhysRevD.72.065015
Faizal, M., Mandal, B.P. and Upadhyay, S.
(2013) Finite BRST Transformations for the Bagger-Lambert-Gustavsson Theory. Physics Letters B, 721, 159-163. http://dx.doi.org/10.1016/j.physletb.2013.02.057
Awad, A. and Ali, A.F. (2014) Minimal Length,
Friedmann Equations and Maximum Density. Journal
of High Energy Physics, 2014, 93. http://dx.doi.org/10.1007/JHEP06(2014)093
Chang-Young, E., Kim,
H. and Nakajima, H. (2008) Noncommutative Superspace and Super Heisenberg
Group. Jour- nal
of High Energy Physics, 2008,
004. http://dx.doi.org/10.1088/1126-6708/2008/04/004
Das, S., Robbins, M.P. and Walton, M.A. (2014) Generalized
Uncertainty Principle Corrections to the Simple Harmonic Oscillator in Phase
Space. arXiv:1412.6467
Majumder,
B. (2013) Quantum Rainbow Cosmological Model with Perfect Fluid. International Journal of Modern Physics D,
22, Article ID:
1350079. http://dx.doi.org/10.1142/S021827181350079X
Gangopadhyay,
S., Dutta, A. and Faizal, M. (2015) Constraints on the Generalized Uncertainty
Principle from Black Hole Thermodynamics. arXiv:1501.01482
Pramanik, S., Faizal, M., Moussa, M. and Ali, A.F.
(2014) The Path Integral Quantization Corresponding to the Deformed Heisenberg
Algebra. arXiv:1411.4979
Ali, A.F., Faizal, M. and
Khalil, M.M. (2014) Remnants of Black Rings from Gravity’s Rainbow. Journal of High Energy Physics, 2014, 159. http://dx.doi.org/10.1007/JHEP12(2014)159
Majumder,
B. and Sen, S. (2012) Do the Modified Uncertainty Principle and Polymer Quantization
Predict Same Physics? Physics Letters B,
717, 291-294. http://dx.doi.org/10.1016/j.physletb.2012.09.035