CRITICAL DIMENSION FOR THE SIEGEL ACTION WITH SUPERSYMMETRIC CHIRAL BOSONS ON GROUP MANIFOLDS

1989 ◽  
Vol 04 (03) ◽  
pp. 701-717 ◽  
Author(s):  
FENG YU ◽  
YONG-SHI WU
Keyword(s):  
Light Cone ◽  
Critical Dimension ◽  
Space Time ◽  
Pathological Feature ◽  
World Sheet ◽  
Anomaly Cancellation ◽  
Light Cone Gauge ◽  
Critical Dimensions ◽  
Covariant Approach ◽  
Chiral Bosons

A classical covariant action which has the Siegel symmetry is constructed for supersymmetric chiral bosons in arbitrary curved space-time coupled to (1,0) world-sheet supergravity. The critical dimension is derived by two methods for such an action with leftons and rightons compactified on group manifolds GL × GR, i.e. by requiring either the closure of the Lorentz algebra in the uncompactified Minkowski space-time in the light-cone gauge approach or the cancellation of both the Siegel and conformal anomalies in the covariant approach. It turns out that the results in the two approaches generally do not agree with each other; in particular, some critical dimensions allowed in the light-cone gauge approach do not lead to anomaly cancellation in the covariant approach. This disagreement represents a pathological feature of Siegel's covariant approach (with usual gauge-fixing procedure) to supersymmetric chiral bosons.

THE SPINNING MEMBRANE, SUPER-SU(∞)-GAUGE THEORIES AND MOYAL BRACKETS

1992 ◽  
Vol 07 (03) ◽  
pp. 535-561
Author(s):  
CARLOS CASTRO
Keyword(s):  
Light Cone ◽  
Fixed Time ◽  
Field Configuration ◽  
Space Time ◽  
Vacuum Field ◽  
World Sheet ◽  
Membrane Action ◽  
Light Cone Gauge ◽  
Yang Mills ◽  
Supersymmetric Gauge

Several important topics concerning the membrane and its symmetries are discussed. The fact that a space–time-independent Lagrangian density for a gauge-field configuration of a (d – 1)-dimensional SU (∞) super Yang–Mills theory, reduced to one dimension (time), is equivalent to a Green–Schwarz formalism of the Euclidean Eguchi–Schild string action in d – 1 dimensions, naturally raises the question whether one can construct a Neveu–Ramond–Schwarz analog. The answer is in the negative; the world-sheet supersymmetric extension of the Eguchi–Schild action for the string cannot be viewed as a classical-vacuum configuration of a super-SU (∞)- gauge theory. For the second topic we construct a "supersymmetry" charge operator, Qf, which plays the role of a residual fermionic symmetry, for fixed time, of the light-cone spinning membrane. It is explicitly shown how the Yang–Mills type of actions and, in particular, the ones for vacuum-field configurations, associated with Q(∞) supergauge theories, are invariant under both Qf "supersymmetry" and the superalgebra of area-preserving superdiffeomorphisms of the light-cone spinning torus membrane, Q(∞). More general actions can be constructed which are invariant under deformations of this superalgebra. In this case the ordinary (graded) Poisson brackets are replaced by super Moyal brackets. Finally, we conjecture why these actions, in analogy with what happens with the light-cone supermembrane, should correspond to a superfiber bundle (over space–time) formulation of the supersymmetric-gauge quantum-mechanical models (SGQMM's) of Flume and Baake et al.; with the general supergroup of trigonometric structure constants of Fairlie, Fletcher and Zachos as the structure supergroup of the superfiber. To support our concluding conjecture, preliminary steps are outlined which are necessary in order to fix the light-cone gauge for the spinning-membrane action. We discuss why the Qf "supersymmetry" (the remnant world-volume light-cone local supersymmetry) and the Q(∞) supergauge transformations must arise as its residual symmetries.

scholarly journals Flat self-dual gravity

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Kirill Krasnov ◽  
Evgeny Skvortsov
Keyword(s):  
Light Cone ◽  
Space Time ◽  
Kinetic Term ◽  
Light Cone Gauge ◽  
Yang Mills ◽  
Covariant Action ◽  
Chiral Interaction ◽  
Double Copy

Abstract We construct a new covariant action for “flat” self-dual gravity in four space-time dimensions. The action has just one term, but when expanded around an appropriate background gives rise to a kinetic term and a cubic interaction. Upon imposing the light-cone gauge, the action reproduces the expected chiral interaction of Siegel. The new action is in many ways analogous to the known covariant action for self-dual Yang-Mills theory. There is also a sense in which the new self-dual gravity action exhibits the double copy of self-dual Yang-Mills structure.

scholarly journals EXACT SOLUTIONS TO THE TWO-DIMENSIONAL BF AND YANG–MILLS THEORIES IN THE LIGHT-CONE GAUGE

2002 ◽  
Vol 17 (11) ◽  
pp. 1491-1502 ◽  
Author(s):  
MITSUO ABE ◽  
NOBORU NAKANISHI
Keyword(s):  
Exact Solution ◽  
Quantum Gravity ◽  
Light Cone ◽  
Lagrangian Density ◽  
Critical Dimension ◽  
Two Dimensional ◽  
Light Cone Gauge ◽  
Yang Mills ◽  
Bf Theory ◽  
Conformal Gauge

It is shown that the BRS (= Becchi–Rouet–Stora)-formulated two-dimensional BF theory in the light-cone gauge (coupled with chiral Dirac fields) is solved very easily in the Heisenberg picture. The structure of the exact solution is very similar to that of the BRS-formulated two-dimensional quantum gravity in the conformal gauge. In particular, the BRS Noether charge has anomaly. Based on this fact, a criticism is made on the reasoning of Kato and Ogawa, who derived the critical dimension D=26 of string theory on the basis of the anomaly of the BRS Noether charge. By adding the [Formula: see text] term to the BF-theory Lagrangian density, the exact solution to the two-dimensional Yang–Mills theory is also obtained.

scholarly journals A NOTE ON 2D CHIRAL GRAVITY AND CHIRAL BOSONS

1992 ◽  
Vol 07 (40) ◽  
pp. 3777-3782 ◽  
Author(s):  
FIORENZO BASTIANELLI
Keyword(s):  
Effective Action ◽  
Light Cone ◽  
Two Dimensional ◽  
Light Cone Gauge ◽  
Conformal Gauge ◽  
Chiral Bosons

Quantization of two-dimensional chiral matter coupled to gravity induces an effective action for the zweibein field which is both Weyl and Lorentz anomalous. Recently, the quantization of this induced action has been analyzed in the light-cone gauge as well as in the conformal gauge. An apparent mismatch between the results obtained in the two gauges is analyzed and resolved by properly treating the Lorentz field as a chiral boson.

CONSTRUCTING THE SUPERSTRING SPACE-TIME SUSY ALGEBRA IN THE LIGHT-CONE GAUGE

1988 ◽  
Vol 03 (12) ◽  
pp. 2855-2893 ◽  
Author(s):  
A. RESTUCCIA ◽  
J.G. TAYLOR
Keyword(s):  
Light Cone ◽  
Explicit Construction ◽  
Space Time ◽  
Substantial Part ◽  
Type I ◽  
Type Ii ◽  
Contact Interactions ◽  
Regularization Scheme ◽  
Light Cone Gauge

Closure of the [10] SUSY algebra is attempted for heterotic and type II superstrings by explicit construction of the quartic supersymmetry and Hamiltonian generators. These are shown to possess only contact interactions. Other related nonlinearly realized generators are also constructed at the quartic level, and a substantial part of the [10]-SUSY algebra shown to close with only these generators, for any regularization scheme for the heterotic, and by using phase integration for the type II. Type I superstrings are also considered.

scholarly journals QUANTIZATION OF BOSONIC STRING MODEL IN (26+2)-DIMENSIONAL SPACE–TIME

2004 ◽  
Vol 19 (12) ◽  
pp. 1923-1959 ◽  
Author(s):  
TAKUYA TSUKIOKA ◽  
YOSHIYUKI WATABIKI
Keyword(s):  
Dimensional Space ◽  
String Model ◽  
Space Time ◽  
Bosonic String ◽  
World Sheet ◽  
Light Cone Gauge ◽  
Weyl Invariance ◽  
Background Space ◽  
Dimensional Space Time ◽  
Gauge Formulation

We investigate the quantization of the bosonic string model which has a local U (1) V × U (1) A gauge invariance as well as the general coordinate and Weyl invariance on the world-sheet. The model is quantized by Lagrangian and Hamiltonian BRST formulations á la Batalin, Fradkin and Vilkovisky and noncovariant light-cone gauge formulation. Upon the quantization the model turns out to be formulated consistently in (26+2)-dimensional background space–time involving two time-like coordinates.

ON THE INFINITIES OF CLOSED SUPERSTRING AMPLITUDES

1988 ◽  
Vol 03 (09) ◽  
pp. 883-892 ◽  
Author(s):  
A. RESTUCCIA ◽  
J.G. TAYLOR
Keyword(s):  
Field Theory ◽  
Light Cone ◽  
Green's Functions ◽  
Green’S Functions ◽  
Type Ii ◽  
World Sheet ◽  
Light Cone Gauge

We present an analysis of possible infinities that may be present in uncompactified multi-loop heterotic and type II superstring amplitudes constructed, without use of the short-string limit, in the light-cone gauge, and with use of a closed [10]-SUSY field theory algebra. Various types of degenerations of the integrand are discussed on the string world-sheet. No infinities are found, modulo (for type II) a particular identity for Green’s functions.

TOPOLOGICAL CONFORMAL ALGEBRA IN POLYAKOV’S LIGHT-CONE GAUGE GRAVITY

1992 ◽  
Vol 07 (35) ◽  
pp. 3291-3302 ◽  
Author(s):  
KIYONORI YAMADA
Keyword(s):  
Light Cone ◽  
Matter Field ◽  
Conformal Algebra ◽  
Two Dimensional ◽  
Topological Algebras ◽  
Light Cone Gauge ◽  
Brst Cohomology ◽  
Dimensional Gravity ◽  
Conformal Gauge ◽  
Gauge Gravity

We show that the two-dimensional gravity coupled to c=−2 matter field in Polyakov’s light-cone gauge has a twisted N=2 superconformal algebra. We also show that the BRST cohomology in the light-cone gauge actually coincides with that in the conformal gauge. Based on this observation the relations between the topological algebras are discussed.

EQUIVALENCE OF TWO-DIMENSIONAL GRAVITIES

1990 ◽  
Vol 05 (16) ◽  
pp. 1251-1258 ◽  
Author(s):  
NOUREDDINE MOHAMMEDI
Keyword(s):  
Gauge Theory ◽  
Explicit Solution ◽  
Light Cone ◽  
Equations Of Motion ◽  
Two Dimensional ◽  
Induced Gravity ◽  
Light Cone Gauge ◽  
Dimensional Gravity ◽  
The Relationship ◽  
Chern Simons

We find the relationship between the Jackiw-Teitelboim model of two-dimensional gravity and the SL (2, R) induced gravity. These are shown to be related to a two-dimensional gauge theory obtained by dimensionally reducing the Chern-Simons action of the 2+1 dimensional gravity. We present an explicit solution to the equations of motion of the auxiliary field of the Jackiw-Teitelboim model in the light-cone gauge. A renormalization of the cosmological constant is also given.

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