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arXiv 0903.4638hep-th
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各种表示的费米子规范理论的SU（N）的Phase diagrams

Phase diagrams of SU(N) gauge theories with fermions in various representations

Joyce C. Myers, Michael C. Ogilvie

备注：
39 pages, 26 figures, JHEP3; references added, small corrections made
发表信息：
JHEP 0907:095,2009
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摘要：

我们最小化SU（N）规范理论的单圈有效势，包括费米子与有限质量的基本（F），伴随（Adj），对称（S），反对称（AS）表示。我们计算了S^1 x R^3上的相图，它是紧致维长度β和费米子质量m的函数。我们考虑了周期边界条件[PBC（+）]和反周期边界条件[ABC（-）]对费米子的影响。PBC（+）的使用产生丰富的相结构。这些相位由Polyakov环P的本征值来区分。QCD（AS/S，+）的有效势的最小化导致相位，其中|Im Tr P|最大化，导致对于所有N和（m β）的所有值的电荷共轭（C）对称性破缺，然而，配分函数直到O（1/N）校正时与应用ABC时相同。因此，关于定向折叠平面等价，我们认为在单圈近似下，PBC应用于费米子所导致的QCD（AS/S，+）中的C-破缺并不使与QCD（Adj，-）的大N等价失效。类似地，对于轨道折叠平面等价，PBC应用于双基本（BF）表象费米子所导致的Z（2）交换对称性的破缺并不使与QCD（Adj，-）在单圈微扰极限下的等价性失效，因为QCD（BF，-）和QCD（BF，+）的配分函数是相同的。特别令人感兴趣的是伴随费米子的情况，其中对于Nf > 1，对于足够小的（m β）获得马约拉纳味限制，并且对于足够大的（m β）获得解除限制。对于N >= 3，这两个相被一个或多个附加相分开，其中一些可以被表征为部分限制相。

英文摘要：

We minimize the one-loop effective potential for SU(N) gauge theories including fermions with finite mass in the fundamental (F), adjoint (Adj), symmetric (S), and antisymmetric (AS) representations. We calculate the phase diagram on S^1 x R^3 as a function of the length of the compact dimension, beta, and the fermion mass, m. We consider the effect of periodic boundary conditions [PBC(+)] on fermions as well as antiperiodic boundary conditions [ABC(-)]. The use of PBC(+) produces a rich phase structure. These phases are distinguished by the eigenvalues of the Polyakov loop P. Minimization of the effective potential for QCD(AS/S,+) results in a phase where | Im Tr P | is maximized, resulting in charge conjugation (C) symmetry breaking for all N and all values of (m beta), however, the partition function is the same up to O(1/N) corrections as when ABC are applied. Therefore, regarding orientifold planar equivalence, we argue that in the one-loop approximation C-breaking in QCD(AS/S,+) resulting from the application of PBC to fermions does not invalidate the large N equivalence with QCD(Adj,-). Similarly, with respect to orbifold planar equivalence, breaking of Z(2) interchange symmetry resulting from application of PBC to bifundamental (BF) representation fermions does not invalidate equivalence with QCD(Adj,-) in the one-loop perturbative limit because the partition functions of QCD(BF,-) and QCD(BF,+) are the same. Of particular interest as well is the case of adjoint fermions where for Nf > 1 Majorana flavour confinement is obtained for sufficiently small (m beta), and deconfinement for sufficiently large (m beta). For N >= 3 these two phases are separated by one or more additional phases, some of which can be characterized as partially-confining phases.

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