RENORMALIZATION IN TRUNCATED PARISI-SOURLAS MODEL

1995 ◽  
Vol 10 (11) ◽  
pp. 859-866
Author(s):  
MYUNG-HOON CHUNG
Keyword(s):  
Vector Field ◽  
Critical Exponents ◽  
Dimensional Regularization ◽  
Vector Model ◽  
Loop Order ◽  
Regularization Scheme ◽  
N Vector

The Parisi-Sourlas model is truncated by ignoring irrelevant terms and introducing an N-vector field. The β-functions for the model of 4−ε dimensions are calculated up to two-loop order in the dimensional regularization scheme. By using the β-functions, the critical exponents are evaluated up to ε2-order. The critical exponents of the truncated Parisi-Sourlas model are compared with those of the ordinary N-vector model. It is found that this model roughly corresponds to the (N−2)-vector model. In fact, the ghost-like fields contribute to the critical exponents in the opposite way, being contrasted with the ordinary N-vector field.

ANOMALOUS DIMENSIONS OF SOFT OPERATORS IN SUPERSYMMETRIC NONLINEAR SIGMA-MODELS

1993 ◽  
Vol 08 (40) ◽  
pp. 3845-3852
Author(s):  
KAY JÖRG WIESE
Keyword(s):  
Sigma Models ◽  
Wide Class ◽  
Vector Model ◽  
Supersymmetric Model ◽  
Harmonic Polynomials ◽  
Loop Order ◽  
Anomalous Dimensions ◽  
Bosonic Model ◽  
N Vector ◽  
Nonlinear Sigma Models

The renormalization ζ-function for supersymmetric nonlinear sigma-models is calculated up to three-loop order. For a wide class of models, which includes the N-vector model and matrix models, the result can be summarized as follows: If the ζ-function for the bosonic model is [Formula: see text], then the ζ-function for the supersymmetric model takes the form [Formula: see text]. This is the case for arbitrary harmonic polynomials of the field variables (so called "soft operators").

SHORT-TIME DYNAMICS OF THE RANDOM n-VECTOR MODEL WITH LONG-RANGE INTERACTION

2003 ◽  
Vol 17 (23) ◽  
pp. 1227-1236 ◽  
Author(s):  
YUAN CHEN ◽  
ZHI-BING LI
Keyword(s):  
Long Range ◽  
High Temperature Phase ◽  
Vector Model ◽  
Temperature Phase ◽  
Range Interaction ◽  
Time Dynamics ◽  
Long Range Interaction ◽  
Renormalization Group Approach ◽  
Short Time ◽  
N Vector

The short-time critical behavior of the random n-vector model with long-range interaction is studied by the theoretic renormalization-group approach. After a sudden quench to the critical temperature from the high temperature phase, the system is released to an evolution within model A dynamics. The initial slip exponents and the dynamic exponent are calculated to two-loop order.

Crossover exponent of the anisotropic n-vector model

1974 ◽  
Vol 47 (5) ◽  
pp. 383-384 ◽  
Author(s):  
R. Oppermann
Keyword(s):  
Vector Model ◽  
N Vector

scholarly journals A prescription for projectors to compute helicity amplitudes in D dimensions

2021 ◽  
Vol 81 (5) ◽  
Author(s):  
Long Chen
Keyword(s):  
Dimensional Regularization ◽  
Tensor Decomposition ◽  
Regularization Scheme ◽  
Lorentz Index ◽  
Dimensional Splitting ◽  
Lorentz Tensor ◽  
Helicity Amplitudes ◽  
Amplitude Level ◽  
Infrared Singularities

AbstractThis article discusses a prescription to compute polarized dimensionally regularized amplitudes, providing a recipe for constructing simple and general polarized amplitude projectors in D dimensions that avoids conventional Lorentz tensor decomposition and avoids also dimensional splitting. Because of the latter, commutation between Lorentz index contraction and loop integration is preserved within this prescription, which entails certain technical advantages. The usage of these D-dimensional polarized amplitude projectors results in helicity amplitudes that can be expressed solely in terms of external momenta, but different from those defined in the existing dimensional regularization schemes. Furthermore, we argue that despite being different from the conventional dimensional regularization scheme (CDR), owing to the amplitude-level factorization of ultraviolet and infrared singularities, our prescription can be used, within an infrared subtraction framework, in a hybrid way without re-calculating the (process-independent) integrated subtraction coefficients, many of which are available in CDR. This hybrid CDR-compatible prescription is shown to be unitary. We include two examples to demonstrate this explicitly and also to illustrate its usage in practice.

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