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Prog. Theor. Phys. Vol. 110 No. 6 (2003) pp. 1117-1150

[ Full Text PDF : FREE ACCESS (303K) ]

N=1 Supersymmetric Yang-Mills Theory in Itō Calculus

Naohito Nakazawa

High Energy Accelerator Research Organization (KEK), Tsukuba 305-0801, Japan

(Received July 30, 2003)

Abstract:

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 Itō 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 SYM4 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 SYM10, the IIB matrix model is studied in this context.


URL : http://ptp.ipap.jp/link?PTP/110/1117/
DOI : 10.1143/PTP.110.1117

[ Full Text PDF : FREE ACCESS (303K) ] Citation:

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Citing Article(s) :

  1. Progress of Theoretical Physics Vol. 116 No. 2 (2006) pp. 349-362 :
    Derivation of Superconformal Anomaly without Ghosts in N = 1 SYM4
    Naohito Nakazawa
  2. Progress of Theoretical Physics Vol. 116 No. 5 (2006) pp. 883-917 :
    Stochastic Gauge Fixing for N = 1 Supersymmetric Yang-Mills Theory
    Naohito Nakazawa

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