Noncommutative Superspace, N=1/2 Supersymmetry, Field Theory and String Theory

Abstract

We deform the standard four dimensional $\mathbb{N}=1$ superspace by making the odd coordinates $\theta$ not anticommuting, but satisfying a Clifford algebra. Consistency determines the other commutation relations of the coordinates. In particular, the ordinary spacetime coordinates $x$ cannot commute. We study chiral superfields and vector superfields and their interactions. As in ordinary noncommutative field theory, a change of variables allows us to express the gauge interactions in terms of component fields which are subject to standard gauge transformation laws. Unlike ordinary noncommutative field theories, the change of the Lagrangian is a polynomial in the deformation parameter. Despite the deformation, the noncommutative theories still have an antichiral ring with all its usual properties. We show how these theories with precisely this deformation arise in string theory in a graviphoton background.

19 pages

Cited by in corpus (187)

• Noncommutative Geometry and Gravity
• Exact Solution of Quantum Field Theory on Noncommutative Phase Spaces
• Superstrings in Graviphoton Background and N=1/2+3/2 Supersymmetry
• Comments on Noncommutative Superspace
• Supersymmetric Gauge Theories on Noncommutative Superspace
• Instanton calculus in R-R background and the topological string
• N=1/2 Wess-Zumino model is renormalizable
• Two-loop Renormalization for Nonanticommutative N=1/2 Supersymmetric WZ Model
• Deformed Superspace, N=1/2 Supersymmetry and (Non)Renormalization Theorems
• Supersymmetry in noncommutative superspaces
• Renormalizability of N=1/2 Wess-Zumino model in superspace
• Nilpotent deformations of N=2 superspace
• Renormalizability of Non(anti)commutative Gauge Theories with N=1/2 Supersymmetry
• Non-anticommutative N=2 super-Yang-Mills theory with singlet deformation
• Towards the Quantum Geometry of the M5-brane in a Constant C-Field from Multiple Membranes
• F-theory and Dark Energy
• Wilsonian Proof for Renormalizability of N=1/2 Supersymmetric Field Theories
• Non(anti)commutative Superspace, UV/IR Mixing & Open Wilson Lines
• Noncommutative Superspace, Supermatrix and Lowest Landau Level
• Non-anticommutative chiral singlet deformation of N=(1,1) gauge theory
• Supersymmetric Quantum Hall Effect on Fuzzy Supersphere
• M-Theory on Deformed Superspace
• N=1/2 gauge theory and its instanton moduli space from open strings in R-R background
• Fuzzy Supersphere and Supermonopole
• Drinfeld-Twisted Supersymmetry and Non-Anticommutative Superspace
• One-Loop Perturbative Corrections to non(anti)commutativity Parameter of N=1/2 Supersymmetric U(N) Gauge Theory
• Marginal Deformations of N=4 SYM from Open/Closed Twistor Strings
• Noncommutativity due to spin
• Sim(2) and SUSY
• On Instantons and Zero Modes of N=1/2 SYM Theory
• Proof of all-order finiteness for planar beta-deformed Yang-Mills
• One-loop renormalisation of N=1/2 supersymmetric gauge theory
• N=2 Supersymmetric U(1) Gauge Theory in Noncommutative Harmonic Superspace
• U(N) Instantons on N=1/2 superspace -- exact solution & geometry of moduli space
• Quantum Hall Liquid on a Noncommutative Superplane
• On a ${\mathbb{Z}}_2^n$-Graded Version of Supersymmetry
• Massless and Massive Three Dimensional Super Yang-Mills Theory and Mini-Twistor String Theory
• Twist-Deformed Supersymmetries in Non-Anticommutative Superspaces
• Cryptogauge symmetry and cryptoghosts for crypto-Hermitian Hamiltonians
• Noncommutative spacetime symmetries: Twist versus covariance
• Comments on Gluino Condensates in N=1/2 SYM Theory
• N=1/2 quiver gauge theories from open strings with R-R fluxes
• Deformation of the ABJM Theory
• Non-anticommutativity in Presence of a Boundary
• Gauge Theory on Noncommutative Supersphere from Supermatrix Model
• On nonanticommutative N=2 sigma-models in two dimensions
• Cyclicity of non-associative products on D-branes
• Non-anticommutative deformation of N=(1,1) hypermultiplets
• Perturbative Quantum Gravity on Complex Spacetime
• Singlet Deformation and Non(anti)commutative N=2 Supersymmetric U(1) Gauge Theory
• One-loop renormalisation of general N=1/2 supersymmetric gauge theory
• D=2, N=2, Supersymmetric theories on Non(anti)commutative Superspace
• Constraint and Super Yang-Mills Equations on the Deformed Superspace R^(4|16)_\hbar
• Non(anti)commutative SYM theory: Renormalization in superspace
• Superfield theory and supermatrix model
• D=2, N=2 Supersymmetric sigma models on Non(anti)commutative Superspace
• Non(anti)commutative N=2 Supersymmetric Gauge Theory from Superstrings in the Graviphoton Background
• The BV Formalization of Chern-Simons Theory on Deformed Superspace
• Non-singlet Q-deformation of the N=(1,1) gauge multiplet in harmonic superspace
• Super-Yang-Mills Theory in SIM(1) Superspace
• Non-Anti-Commutative deformation of effective potentials in supersymmetric gauge theories
• Non-local Wess-Zumino Model on Nilpotent Noncommutative Superspace
• The three-dimensional non-anticommutative superspace
• BPS-type equations in the non-anticommutative N=2 supersymmetric U(1) gauge theory
• Instanton Calculations for N=1/ 2 super Yang-Mills Theory
• Jordanian Quantum Deformations of D=4 Anti-de-Sitter and Poincare Superalgebras
• Supersymmetric quantum mechanics on noncommutative space
• Chiral effective potential in $\mathcal{N}=1/2$ non-commutative Wess-Zumino model
• Deformed Supersymmetry in Non(anti)commutative N=2 Supersymmetric U(1) Gauge Theory
• Field Theory in Noncommutative Minkowski Superspace
• Gauged Wess-Zumino Model in Noncommutative Minkowski Superspace
• Boundary Effects in the BLG Theory
• Spectral Degeneracy in Supersymmetric Gluodynamics and One-Flavor QCD related to N=1/2 SUSY
• Nonanticommutative superspace and N= 1/2 WZ model
• Aspects of ABJ Theory
• Non-commutative (D)-instantons
• Superstar in Noncommutative Superspace via Covariant Quantization of the Superparticle
• Non(anti)commutative N=(1,1/2) Supersymmetric U(1) Gauge Theory
• Chern-Simons Theory in SIM(1) Superspace
• Non-anticommutative ABJ Theory
• Field Theory on Nonanticommutative Superspace
• Non-anticommutative N=2 supersymmetric SU(2) gauge theory
• Deformed N=1 supersymmetry
• Deformation of N=4 Super Yang-Mills Theory in Graviphoton Background
• Seiberg-Witten Map for Superfields on Canonically Deformed N=1, d=4 Superspace
• Godel Spacetimes, Abelian Instantons, the Graviphoton Background and other Flacuum Solutions
• CP-violating super Weyl anomaly
• Hermitian versus holomorphic complex and quaternionic generalized supersymmetries of the M-theory. A classification
• Weyl-Wigner-Moyal Formalism for Fermi Classical Systems
• Seiberg-Witten Map for Superfields on N=(1/2,0) and N=(1/2,1/2) Deformed Superspace
• Deformation of Super Yang-Mills Theories in R-R 3-form Background
• Flux Vacua and Supermanifolds
• Quantum Corrections in 2D SUSY CP^{N-1} Sigma Model on Noncommutative Superspace
• N=2 sigma model Action on Non(anti)commutative Superspace
• N=1/2 Super Yang-Mills Theory on Euclidean AdS2xS2
• Ring Structure of SUSY * Product and 1/2 SUSY Wess-Zumino Model
• Konishi Anomaly and Central Extension in N=1/2 Supersymmetry
• On Non-linear Action for Gauged M2-brane
• Cryptoreality of nonanticommutative Hamiltonians
• N=1/2 Deformations of Chiral Superspaces from New Quantum Poincare and Euclidean Superalgebras
• One-loop renormalisation of N=1/2 supersymmetric gauge theory with a superpotential
• Supersymmetric Chern-Simons Theory and Supersymmetric Quantum Hall Liquid
• Chiral Models in Noncommutative N=1/2 Four Dimensional Superspace
• Note on a fermionic solution of the matrix model and noncommutative superspace
• The Supersymmetric (2+1)D Noncommutative $C{P}^{(N-1)}$ Model in the Fundamental Representation
• Nonanticommutative Deformation of N=4 SYM Theory: The Myers Effect and Vacuum States
• Construction of the effective action in nonanticommutative supersymmetric field theories
• The non-anticommutative supersymmetric Wess-Zumino model
• Non(anti)commutative superspace with coordinate-dependent deformation
• Partial $\mathcal{N}=2\to \mathcal{N}=1$ supersymmetry breaking and gravity deformed chiral rings
• Note on Gauge Theory on Fuzzy Supersphere
• N=1/2 supersymmetric four-dimensional non-linear sigma-models from non-anti-commutative superspace
• Supersymmetric large-N reduced model with multiple matter
• Deformed conformal and super-Poincaré symmetries in the non-(anti)commutative spaces
• Superloop Space
• Non(anti)commutative N=2 Supersymmetric U(N) Gauge Theory and Deformed Instanton Equations
• Noncommutative Superspace and Super Heisenberg Group
• Renormalizability of non-anticommutative N=(1,1) theories with singlet deformation
• Renormalisation of supersymmetric gauge theory in the uneliminated component formalism
• N=2 Superparticles, RR Fields and Noncommutative Structures of (super)-Spacetime
• Effective actions, Wilson lines and the IR/UV mixing in noncommutative supersymmetric gauge theories
• Non-singlet Q-deformed N=(1,0) and N=(1,1/2) U(1) actions
• On chiral quantum superspaces
• The Hamiltonian structure of a coupled system derived from a supersymmetric breaking of Super KdV equations
• Recovery of Full N=1 Supersymmetry in Non(anti-)commutative Superspace
• Isometric Embeddings and Noncommutative Branes in Homogeneous Gravitational Waves
• N=1/2 supergravity with matter in four Euclidean dimensions
• A renormalizable N=1/2 SYM theory with interacting matter
• Summing up Non-anti-commutative Kaehler potential
• Nilpotent noncommutativity and renormalization
• Deformations of Euclidean Supersymmetries
• Instantons and Matter in N=1/2 Supersymmetric Gauge Theory
• Instanton Calculus in R-R 3-form Background and Deformed N=2 Super Yang-Mills Theory
• D-deformed Wess-Zumino model and its renormalizability properties
• Instanton Calculus in Deformed N=4 Super Yang-Mills Theories
• Gauge theory in deformed N=(1,1) superspace
• Hybrid Formalism, Supersymmetry Reduction, and Ramond-Ramond Fluxes
• On the Seiberg-Witten map of $\mathcal{N}=2$ SYM theory in Non(anti)commutative Harmonic Superspace
• Monopoles in Superloop Space
• Deformed matrix models, supersymmetric lattice twists and N=1/4 supersymmetry
• Soft-Collinear Supersymmetry
• Hamiltonian structure and noncommutativity in $p$-brane models with exotic supersymmetry
• One-loop effective potential in $\mathcal{N}=1/2$ generic chiral superfield model
• One-loop divergences in the two-dimensional non-anticommutative supersymmetric sigma-model
• C-deformation of Supergravity
• AdS/CFT Duality for Non-Anticommutative Supersymmetric Gauge Theory
• Real and pseudoreal forms of D=4 complex Euclidean (super)algebras and super-Poincare / super-Euclidean r-matrices
• Quantum Mechanics in Non(Anti)Commutative Superspace
• The non-anticommutative supersymmetric U(1) gauge theory
• Physics of crypto-Hermitian and/or cryptosupersymmetric field theories
• Non-anticommutative Supersymmetric Field Theory and Quantum Shift
• Deformation Quantization of Fermi Fields
• Supersymmetric Nambu$-$Jona-Lasinio Model on $\mathcal{N}=1/2$ four-dimensional Non(anti)commutative Superspace
• (Non)renormalizability of the D-deformed Wess-Zumino model
• Instantons in N=1/2 Super Yang-Mills Theory via Deformed Super ADHM Construction
• Non-abelian vector backgrounds with restored Lorentz invariance
• Lorentz invariant ensembles of vector backgrounds
• On A Superfield Extension of The ADHM Construction and N=1 Super Instantons
• Black Hole Partition Function using Hybrid Formalism of Superstrings
• N=1/2 Supersymmetric gauge theory in noncommutative space
• Nonanticommutative U(1) SYM theories: Renormalization, fixed points and infrared stability
• All-Loop Renormalizable Wess-Zumino Model on Bosonic-Fermionic Noncommutative Superspace
• Finite Supersymmetry Transformations
• A coordinate-dependent superspace deformation from string theory
• Supersymmetric Duality in Deformed Superloop Space
• SUSY Quantum Hall Effect on Non-Anti-Commutative Geometry
• Morita Equivalence of Noncommutative Supertori
• A renormalisable non-anticommutative SU(N)xU(1) gauge theory in components
• Central Charges in Non(anti)commutative N=2 Supersymmetric U(N) Gauge Theory
• Global Space-Time Symmetries of Quantized Euclidean and Minkowski Superspaces
• Degeneracies in Supersymmetric Gluodynamics and its Orientifold Daughters at large N
• Fermionic T-duality and Morita Equivalence
• Renormalisation of the non-anticommutativity parameter at two loops
• Vector-multiplet effective action in the non-anticommutative charged hypermultiplet model
• Duality invariance of non-anticommutative N=1/2 supersymmetric U(1) gauge theory
• Twisted Supersymmetry in a Deformed Wess-Zumino Model in (2+1) Dimensions
• Twisted SUSY: twisted symmetry versus renormalizability
• Comments on the role of field redefinition on renormalisation of $N=\frac{1}{2}$ supersymmetric pure gauge theory
• Non-topological non-commutativity in string theory
• On the alternative formulation of the three-dimensional noncommutative superspace
• Non-Anticommutative Deformations of N=(1,1) Supersymmetric Theories
• One-Loop Renormalizable Wess-Zumino Model on Bosonic-Fermionic Noncommutative Superspace
• Supersymmetry breaking in noncommutative quantum mechanics
• The role of field redefinition on renormalisability of a general $N=\frac{1}{2}$ supersymmetric gauge theories
• Deformation quantization for systems with second-class constraints in deformed fermionic phase space
• Noncommutative $\mathcal{N}=2$ Chern-Simons-matter model
• N=1/2 Global SUSY: R-Matrix Approach