SU(N) lattice gauge theory with villain’s action
1981; Springer Nature; Volume: 66; Issue: 3 Linguagem: Inglês
10.1007/bf02731690
ISSN0369-3546
Autores Tópico(s)Particle physics theoretical and experimental studies
ResumoWe consider the pure gauge lattice theory with Villain's action exp $$\left[ { - A\left( U \right)} \right] = \prod\limits_{j = 1}^N {\sum\limits_{n = - \infty }^{ + \infty } {\exp \left[ { - \left( {{N \mathord{\left/ {\vphantom {N \lambda }} \right. \kern-\nulldelimiterspace} \lambda }} \right)\left( {\theta _j + 2n\pi } \right)^2 } \right]} } $$ , where ϑ1, …, ϑ N are the invariant angles ofU ≠U(N) orSU(N). For the two-dimensional lattice we calculate the partition functionZ(λ, N), the specific heat, the level densityϱ N(ϑ) and Wilson's loopsW n=(1/N〈tr(U n)〉 (n=1,2,3,…). The 1/N expansion ofZ andW n is convergent for sufficiently small |λ/N| and its coefficients are analytic inλ near the real axis (no «Gross-Witten» singularity to all orders in 1/N), but it is still not possible to commute the strong-coupling limit with the planar limit (λ → ∞,N → ∞). We also calculate the character expansion which is needed for strong-coupling calculations in four dimensions. A comparison with Monte Carlo data (N=2) and a preliminary discussion of the large-N limit is given.
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