Conformal anomaly for string theory from stochastic quantization

1991 ◽  
Vol 43 (6) ◽  
pp. 2050-2053
Author(s):  
Ki Soo Chung ◽  
Jae Kwan Kim
Keyword(s):  
String Theory ◽  
Conformal Anomaly ◽  
Stochastic Quantization

INDEFINITENESS OF THE CONFORMAL ANOMALY OF THE STRING THEORY IN THE HARMONIC GAUGE

1992 ◽  
Vol 07 (20) ◽  
pp. 1799-1804 ◽  
Author(s):  
MITSUO ABE ◽  
NOBORU NAKANISHI
Keyword(s):  
String Theory ◽  
Quantum Gravity ◽  
Lagrangian Density ◽  
Order Approximation ◽  
Bosonic String ◽  
Conformal Anomaly ◽  
Two Dimensional ◽  
Critical Dimensions ◽  
Total Divergence ◽  
Field Redefinition

The derivation of the critical dimensions D=26 of the bosonic string theory based on the two-dimensional quantum gravity in the harmonic gauge is criticized. The conformal anomaly calculated in lowest-order approximation crucially depends on the presence of a certain part of the FP-ghost Lagrangian density. However, this part can be eliminated by field redefinition and, moreover, reduces to a total divergence in lowest-order approximation. Thus the assertion that the anomaly is proportional to (D−26) is groundless.

scholarly journals HADRONIC STRING, CONFORMAL INVARIANCE AND CHIRAL SYMMETRY

2003 ◽  
Vol 18 (14) ◽  
pp. 2501-2539 ◽  
Author(s):  
J. ALFARO ◽  
L. BALART ◽  
A. A. ANDRIANOV ◽  
D. ESPRIU
Keyword(s):  
String Theory ◽  
Sigma Model ◽  
Conformal Anomaly ◽  
Nonlinear Sigma Model ◽  
Leading Order ◽  
Qcd Vacuum ◽  
Fundamental String ◽  
Supersymmetric Version ◽  
Long Time ◽  
Model Approach

While it is clear that in some kinematic regime QCD can be described by an effective (as opposed to fundamental) string theory, it is not at all clear how this string theory should be. The "natural" candidate, the bosonic string, leads to amplitudes with the usual problems related to the existence of the tachyon, the absence of the adequate Adler zero, and massless vector particles, not to mention the conformal anomaly. The supersymmetric version does not really solve most of these problems. For a long time it has been believed that the solution of at least some of these difficulties is associated to a proper identification of the vacuum, but this program has remained elusive. We show in this work how the first three problems can be avoided, by using a sigma model approach where excitations above the correct (chirally noninvariant) QCD vacuum are identified. At the leading order in a derivative expansion we recover the nonlinear sigma model of pion interactions. At the next-to-leading order the O(p4) Lagrangian of Gasser and Leutwyler is obtained, with values for the coefficients that match the observed values. We also discuss some issues related to the conformal anomaly.

COMMENT ON THE TRACE ANOMALY IN STOCHASTIC QUANTIZATION

1992 ◽  
Vol 07 (10) ◽  
pp. 841-847 ◽  
Author(s):  
NAOHITO NAKAZAWA
Keyword(s):  
Path Integral ◽  
Langevin Equation ◽  
Stochastic Calculus ◽  
Conformal Anomaly ◽  
Stochastic Quantization ◽  
Weyl Invariance ◽  
Trace Anomaly ◽  
Integral Measure ◽  
Coordinate Invariance

We investigate the origin of the trace (conformal) anomaly in the context of stochastic quantization. Based on the Langevin equation, we study the local Ward-Takahashi identities corresponding to the Weyl invariance and the general coordinate invariance. It is shown that the Ito's stochastic calculus essentially picks up the non-trivial Jacobian factor which appears in the path-integral measure. We also provide how to construct the Langevin equation which maintains the general coordinate invariance in consistent with the Ito's calculus.

A Mathematical Introduction to String Theory

1997 ◽  
Author(s):  
Sergio Albeverio ◽  
Jurgen Jost ◽  
Sylvie Paycha ◽  
Sergio Scarlatti
Keyword(s):  
String Theory
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