Chiral symmetry restoration at large chemical potential in strongly coupled SU(N) gauge theories

Reflection positivity in timelike planes, which was invoked in the convergence proof of the type of cluster expansion used in [ 12 ] , no longer holds in the presence of nonvanishing chemical potential

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Whatever (non)convergence properties this 1 / d 1/d expansion may have at physical values of d d , its truncation to leading terms mimics the corresponding truncation in the expansion considered in this paper

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More generally, the global symmetry is G × G G\times G where G G is the subgroup of U ⁡ ( N f ) U(N_{f}) which commutes with all the matrices { γ ⁡ [ b ] } \{\gamma[b]\} . For staggered fermions G = U ⁡ ( N f ) G=U(N_{f})

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On a more technical note, we do not employ any sort of “improved” staggered fermion actions. Indeed, such “improvements” are only designed to assist approach to the continuum limit. They are not suited for our application at strong coupling, finite lattice spacing, where they are generally known to lead to unphysical effects such as spurious phases and other artifacts due to explicit violation of reflection positivity and other undesirable features

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Thus, with parametrization U = exp ⁡ ( i ​ 𝝎 ⋅ 𝐡 ) U=\exp(i\mbox{\boldmath$\omega$}\cdot{\bf h}) , where 𝐡 = ( h 1 , … , h N − 1 ) {\bf h}=(h_{1},\ldots,h_{N-1}) are the S ​ U ​ ( N ) SU(N) Cartan subalgebra generators, one may set θ i = 𝝎 ⋅ 𝐦 i \theta_{i}=\mbox{\boldmath$\omega$}\cdot{\bf m}_{i} , where 𝐦 i {\bf m}_{i} are the fundamental representation root vectors

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Indeed, each connected component of a given set B B may give rise to more than one distinct connected diagram from distinct Wick theorem contractions embodied in the integrations over d ​ μ 𝐱 d\mu_{\bf x} . Different connected components of a given set B B give of course rise to disjoint connected diagrams

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