Yang–Mills integrals for orthogonal, symplectic and exceptional groups
نویسندگان
چکیده
منابع مشابه
Yang-Mills Integrals for Orthogonal, Symplectic and Exceptional Groups
We apply numerical and analytic techniques to the study of Yang-Mills integrals with orthogonal, symplectic and exceptional gauge symmetries. The main focus is on the supersymmetric integrals, which correspond essentially to the bulk part of the Witten index for susy quantum mechanical gauge theory. We evaluate these integrals for D = 4 and group rank up to three, using Monte Carlo methods. Our...
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We consider the action of H = O(p, q) on the matrix space Mp+q,n(R). We study a certain orbit O of H in the null cone N ⊆ Mp+q,n(R) which supports an eigendistribution dνO for H . Using some identities of Capelli type developed in the Appendix, we determine the structure of G̃ = Sp(2n,R)∼-cyclic module generated by dνO under the oscillator representation of G̃ (the metaplectic cover of G = Sp(2n(...
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The Harish-Chandra correlation functions, i.e. integrals over compact groups of invariant monomials ∏ tr ( X1ΩY 1ΩX2 · · · ) with the weight exp tr ( XΩY Ω ) are computed for the orthogonal and symplectic groups. We proceed in two steps. First, the integral over the compact group is recast into a Gaussian integral over strictly upper triangular complex matrices (with some additional symmetries)...
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The projective orthogonal and symplectic groups POn(F ) and PSpn(F ) have a natural action on the F vector space V ′ = Mn(F ) ⊕ . . . ⊕ Mn(F ). Here we assume F is an infinite field of characteristic not 2. If we assume there is more than one summand in V , then the invariant fields F (V )n and F (V )n are natural objects. They are, for example, the centers of generic algebras with the appropri...
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ژورنال
عنوان ژورنال: Nuclear Physics B
سال: 2000
ISSN: 0550-3213
DOI: 10.1016/s0550-3213(00)00382-5