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In particular, this implies that a large $N$ gauge theory which, on $\\R^d$, flows to an IR fixed point, retains the infinite correlation length and other scale invariant properties of the decompactified theory even when compactified on $\\R^{d-k} \\times (S^1)^k$. In other words, finite volume effects are $1/N$ suppressed. 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Yaffe, Mithat Unsal","submitted_at":"2010-06-10T18:10:35Z","abstract_excerpt":"Consequences of large $N$ volume independence are examined in conformal and confining gauge theories. In the large $N$ limit, gauge theories compactified on $\\R^{d-k} \\times (S^1)^k$ are independent of the $S^1$ radii, provided the theory has unbroken center symmetry. In particular, this implies that a large $N$ gauge theory which, on $\\R^d$, flows to an IR fixed point, retains the infinite correlation length and other scale invariant properties of the decompactified theory even when compactified on $\\R^{d-k} \\times (S^1)^k$. In other words, finite volume effects are $1/N$ suppressed. 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