arXiv subjects

Naohito Nakazawa

Publications and source records attributed to Naohito Nakazawa.

9 recordsLinked to original sources

arXiv2006

Stochastic gauge fixing for N = 1 supersymmetric Yang-Mills theory

The gauge fixing procedure for N=1 supersymmetric Yang-Mills theory (SYM) is proposed in the context of the stochastic quantization method (SQM). The stochastic gauge fixing, which was formulated by Zwanziger for Yang-Mills theory, is extended to SYM_4 in the superfield formalism by introducing a chiral and an anti-chiral superfield as the gauge fixing functions. It is shown that SQM with the stochastic gauge fixing reproduces the probability distribution of SYM_4, defined by the Faddeev-Popov prescription, in the equilibrium limit with an appropriate choice of the stochastic gauge fixing functions. We also show that the BRST symmetry of the corresponding stochastic action and the power counting argument in the superfield formalism ensure the renormalizability of SYM_4 in this context.

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arXiv2006

N=1 Super Yang-Mills Theory in Ito Calculus

The stochastic quantization method is applied to N = 1 supersymmetric Yang-Mills theory, in particular in 4 and 10 dimensions. In the 4 dimensional case, based on Ito calculus, the Langevin equation is formulated in terms of the superfield formalism. The stochastic process manifestly preserves both the global N = 1 supersymmetry and the local gauge symmetry. The expectation values of the local gauge invariant observables in SYM_4 are reproduced in the equilibrium limit. In the superfield formalism, it is impossible in SQM to choose the so-called Wess-Zumino gauge in such a way to gauge away the auxiliary component fields in the vector multiplet, while it is shown that the time development of the auxiliary component fields is determined by the Langevin equations for the physical component fields of the vector multiplet in an '' almost Wess-Zumino gauge ''. The physical component expressions of the superfield Langevin equation are naturally extended to the 10 dimensional case, where the spinor field is Majorana-Weyl. By taking a naive zero volume limit of the SYM_10, the IIB matirx model is studied in this context.

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arXiv2006

Derivation of Superconformal Anomaly without Ghosts in N = 1 SYM_4

The anomalous Ward-Takahashi identity for the superconformal symmetry in the four-dimensional N=1 supersymmetric Yang-Mills theory is studied in terms of the stochastic quantization method (SQM). By applying the background field method to the SQM approach, we derive the superconformal anomaly in the one-loop approximation and show that the supersymmetric stochastic gauge fixing term does not contribute to the anomaly.

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arXiv2003

Background Field Method in Stochastic Quantization of N = 1 Supersymmetric Yang-Mills Theory

In the previous works, we proposed the stochastic quantization method (SQM) approach to N=1 supersymmetric Yang-Mills theory (SSYM). In four dimensions, in particular, we obtained the superfield Langevin equation and the corresponding Fokker-Planck equation which describe the underlying stochastic process manifestly preserving the global supersymmetry as well as the local gauge symmetry. The stochastic gauge fixing procedure was also applied to SSYM_4 in the superfield formalism. In this note, we apply the background field methd to SSYM_4 in terms of the stochastic action principle in SQM approach. The one-loop $β$-function for the gauge coupling agrees with that given by the path-integral approach, thereby confirming that the stochastic gauge fixing procedure with the background local gauge invariant Zwanziger's gauge fixing functions simulates the contributions from the Nielsen-Kallosh ghost as well as the Faddeev-Popov ghost at the one-loop level. We also show the equivalence of the stochastic effective action in the background field method to the standard one in SQM.

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arXiv2003

Comment on Geometric Interpretation of Ito Calculus on the Lattice

A covariant nature of the Langevin equation in Ito calculus is clarified in applying stochastic quantization method to U(N) and SU(N) lattice gauge theories. The stochastic process is expressed in a manifestly general coordinate covariant form as a collective field theory on the group manifold. A geometric interpretation is given for the Langevin equation and the corresponding Fokker-Planck equation in the sense of Ito.

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arXiv2002

Note on a Closed String Field Theory from Bosonic IIB Matrix Model

We apply stochastic quantization method to the bosonic part of IIB matrix model, i.e., a naive zero volume limit of large N Yang-Mills theory, to construct a collective field theory of Wilson loops. The Langevin equation for Wilson loops can be interpreted as the time evolution of closed string fields. The corresponding Fokker-Planck hamiltonian deduces a closed string field theory which describes interacting Wilson loops with manifest Lorentz invariance.

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arXiv1999

Algebraic Structure in 0<c<1 Open-Closed String Field Theories

We apply stochastic quantization method to Kostov's matrix-vector models for the second quantization of orientable strings with Chan-Paton like factors, including both open and closed strings. The Fokker-Planck hamiltonian deduces an orientable open-closed string field theory at the double scaling limit. There appears an algebraic structure in the continuum F-P hamiltonian including a Virasoro algebra and a SU(r) current algebra.

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arXiv1997

Algebraic Structure in Non-Orientable Open-Closed String Field Theories

We apply stochastic quantization method to real symmetric matrix-vector models for the second quantization of non-orientable strings, including both open and closed strings. The Fokker-Planck hamiltonian deduces a well-defined non-orientable open-closed string field theory at the double scaling limit of the matrix model. There appears a new algebraic structure in the continuum F-P hamiltonian including a Virasoro algebra and a $SO(r)$ current algebra.

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arXiv1994

Large Improved Wick Rotation Prescription in Stochastic Quantization of Dissipative Systems

We apply Stochastic Quantization Method to dissipative systems at finite temperature. Especially, the relation of SQM to the Caldeira-Leggett model is clarified ensuring that the naive Wick rotation is improved in this context. We show that the Langevin system obtained by the \lq\lq Improved Wick Rotation " prescription is equivalent to an ideal friction case ( low temperature limit) in the C-L model. We derive, based on our approach, a general formula on the fluctuation-dissipation theorem for higher derivative frictions.

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