Gauge theory formulation of the c = 1 matrix model; Symmetries and discrete states

Journal Article · Thu Aug 20 00:00:00 EDT 1992 · International Journal of Modern Physics A; (United States)

DOI:https://doi.org/10.1142/S0217751X92002362· OSTI ID:6967330

Das, S R; Dhar, A ^[1]; Mandal, G ^[2]; Wadia, S R ^[3]

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1. Tata Inst. of Fundamental Research, Homi Bhabha Road, Bombay 400 005 (India)
2. Inst. for Advanced Study, Princeton, NJ (United States)
3. Theoretische Physik, ETH-Honggerberg, 8093 Zurich (Switzerland)

In this paper, the authors present a nonrelativistic fermionic field theory in two dimensions coupled to external gauge fields. The singlet sector of the c = 1 matrix model corresponds to a specific external gauge field. The gauge theory is one-dimensional (time) and the space coordinate is treated as a group index. The generators of the gauge algebra are polynomials in the single particle momentum and position operators and they form the group W [sup (+)][sub 1 + [infinity]]. There are corresponding Ward identities and residual gauge transformations that leave the external gauge fields invariant. The authors discuss the realization of the residual symmetries in the Minkowski time theory and conclude that the symmetries generated by the polynomial basis are not realized. The authors motivate and present an analytic continuation of the model which realizes the group of residual symmetries. The authors consider the classical limit of this theory and make the correspondence with the discrete states of the c = 1 (Euclidean time) Liouville theory. The authors explain the appearance of the SL(2) structure in W[sup (+)][sub 1 + [infinity]]. The authors also present all the Euclidean classical solutions and the classical action in the classical phase space. A possible relation of this theory to the N =2 string theory and also self-dual Einstein gravity in four dimensions is pointed out.

• OSTI ID: 6967330
• Journal Information: International Journal of Modern Physics A; (United States), Vol. 7:21; ISSN 0217-751X
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
FERMIONS
FIELD THEORIES
GAUGE INVARIANCE
ALGEBRA
CORRELATIONS
COUPLING
EUCLIDEAN SPACE
GENERAL RELATIVITY THEORY
PHASE SPACE
POLYNOMIALS
SL GROUPS
STRING MODELS
SYMMETRY
TWO-DIMENSIONAL CALCULATIONS
WARD IDENTITY
COMPOSITE MODELS
EXTENDED PARTICLE MODEL
FUNCTIONS
INVARIANCE PRINCIPLES
LIE GROUPS
MATHEMATICAL MODELS
MATHEMATICAL SPACE
MATHEMATICS
PARTICLE MODELS
QUARK MODEL
RIEMANN SPACE
SPACE
SYMMETRY GROUPS
662110* - General Theory of Particles & Fields- Theory of Fields & Strings- (1992-)
662120 - General Theory of Particles & Fields- Symmetry
Conservation Laws
Currents & Their Properties- (1992-)