Space–time symmetry of noncommutative field theory

We argue that Poincaré symmetry can be implemented in noncommutative field theory (NCFT) if we allow the parameter of noncommutative deformation θμν to change as a two-tensor under the corresponding space–time symmetry. The implementation is consistent with the definition of θμν in terms of space–time coordinates and with the Moyal star product. Inspired by the standard definition of a variational symmetry we found a universal way to correct the implementation of the Poincaré symmetry by a term proportional to the variation of θμν in such a way that the new transformation define a symmetry of the theory. Finally we present as an example the case of NCYM theory and comment about the obstructions to implement generalized space–time symmetries in NCFT-like conformal or diffeomorphism transformations.

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Path integral for space-time noncommutative field theory

Physical Review D ◽

10.1103/physrevd.70.085006 ◽

2004 ◽

Vol 70 (8) ◽

Cited By ~ 27

Author(s):

Kazuo Fujikawa

Keyword(s):

Field Theory ◽

Path Integral ◽

Space Time ◽

Noncommutative Field Theory

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CONFORMAL SYMMETRY OF SUPERSTRINGS ON AdS3 × S3 × T4 AND D1/D5 System

Modern Physics Letters A ◽

10.1142/s0217732302009003 ◽

2002 ◽

Vol 17 (37) ◽

pp. 2477-2485 ◽

Cited By ~ 1

Author(s):

ABBAS ALI

Keyword(s):

Field Theory ◽

Conformal Field Theory ◽

Conformal Symmetry ◽

Space Time ◽

Superconformal Algebra ◽

Superconformal Symmetry ◽

Conformal Field ◽

Time Symmetry

Conformal field theory of the D1/D5 system and superstrings on AdS3 × S3 × T4 is studied with particular attention to the worldsheet fields corresponding to the T4 part. A solution to the space–time N = 4 superconformal symmetry doubling and other problems is proposed. It is argued that the relevant space–time symmetry should be based on the middle N = 4 superconformal algebra. It is discussed as to why this superconformal structure has been missed so far.

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Analyticity Properties and Thermal Effects for General Quantum Field Theory on de Sitter Space-Time

Communications in Mathematical Physics ◽

10.1007/s002200050435 ◽

1998 ◽

Vol 196 (3) ◽

pp. 535-570 ◽

Cited By ~ 46

Author(s):

Jacques Bros ◽

Henri Epstein ORF RID="a3"> ◽

Ugo Moschella

Keyword(s):

Field Theory ◽

Quantum Field Theory ◽

Thermal Effects ◽

De Sitter Space ◽

Space Time ◽

Quantum Field ◽

De Sitter ◽

General Quantum

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ε-EXPANSION IN QUANTUM FIELD THEORY IN CURVED SPACE–TIME

International Journal of Modern Physics A ◽

10.1142/s0217751x98001451 ◽

1998 ◽

Vol 13 (16) ◽

pp. 2857-2874

Author(s):

IVER H. BREVIK ◽

HERNÁN OCAMPO ◽

SERGEI ODINTSOV

Keyword(s):

Field Theory ◽

Quantum Field Theory ◽

Space Time ◽

Quantum Field ◽

Curved Space ◽

Njl Model ◽

Effective Lagrangian ◽

Special Solutions ◽

Curvature Approximation ◽

Symmetric Phase

We discuss ε-expansion in curved space–time for asymptotically free and asymptotically nonfree theories. The existence of stable and unstable fixed points is investigated for fϕ4 theory and SU(2) gauge theory. It is shown that ε-expansion maybe compatible with aysmptotic freedom on special solutions of the RG equations in a special ase (supersymmetric theory). Using ε-expansion RG technique, the effective Lagrangian for covariantly constant gauge SU(2) field and effective potential for gauged NJL model are found in (4-ε)-dimensional curved space (in linear curvature approximation). The curvature-induced phase transitions from symmetric phase to asymmetric phase (chromomagnetic vacuum and chiral symmetry broken phase, respectively) are discussed for the above two models.

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