Phase diagrams of SU(N) gauge theories with fermions in various representations
Phase diagrams of SU(N) gauge theories with fermions in various representations
复制标题
具有各种表示形式的费米子的 SU(N) 规范理论的相图
DOI：
10.1088/1126-6708/2009/07/095
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发表时间：
2009
影响因子：
5.4
通讯作者：
M. Ogilvie
中科院分区：
文献类型：
--
作者：
Joyce C. Myers;M. Ogilvie
在基本(F)、伴随(Adj)、对称(S)和反对称(As)表示下，我们最小化了包括有限质量费米子在内的SU(N)规范理论的单圈有效势。对于不同的N和Nf，我们计算了S1？3上的相图，它是紧致维度长度？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。对于费米子上的标准ABC(-)，对于所考虑的所有表示，只在一个环处发现解禁闭相。然而，PBC(+)的使用产生了丰富的相结构。这些位相由Polyakov环P的本征值来区分。在基本表示费米子[QCD(F，+)]的情况下，对于m的所有值，Re？TrP最小化(和负)的位相是有利的。对于N个奇电荷共轭()，由于(1/N)效应，对称性在这个相中自发破缺。QCD(As/S，+)的有效势的最小化导致了这样一个阶段：|Im？TrP|被最大化，导致对所有N和所有m的值都是破缺的，然而，配分函数直到(1/N)校正都与应用ABC时相同。因此，对于方向平面等价，我们认为在QCD(As/S，+)中由于对费米子应用PBC而导致的单圈近似破缺并不会使大N等价与QCD(Adj，-)失效。类似地，对于OBORBORLD平面等价，由于将PBC应用于双基(BF)表示费米子而导致的Z2交换对称性的破坏并不意味着在单圈微扰极限下与QCD(Adj，-)的等价无效，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，其中对于足够小的m？，对于1$>；nF>；得到1个Majorana味禁闭，而对于足够大的m？，得到去禁闭。对于N？3，这两个相被一个或多个附加相分开，其中一些可以被表征为部分约束相。
We minimize the one-loop effective potential for SU(N) gauge theories including fermions with finite mass in the fundamental (F), adjoint (Adj), symmetric (S), and antisymmetric (AS) representations. We calculate the phase diagram on S1 ? 3 as a function of the length of the compact dimension, ?, and the fermion mass, m, for various N and Nf. We consider the effect of periodic boundary conditions [PBC(+)] on fermions as well as antiperiodic boundary conditions [ABC(-)]. With standard ABC(-) on fermions only the deconfined phase is found at one-loop for all representations considered. However, the use of PBC(+) produces a rich phase structure. These phases are distinguished by the eigenvalues of the Polyakov loop P. In the case of fundamental representation fermions [QCD(F,+)], a phase in which Re?Tr P is minimized (and negative) is favoured for all values of m?. For N odd charge conjugation () symmetry is spontaneously broken in this phase due to (1/N) effects. Minimization of the effective potential for QCD(AS/S,+) results in a phase where |Im?Tr P| is maximized, resulting in -breaking for all N and all values of m?, however, the partition function is the same up to (1/N) corrections as when ABC are applied. Therefore, regarding orientifold planar equivalence, we argue that in the one-loop approximation -breaking in QCD(AS/S,+) resulting from the application of PBC on fermions does not invalidate the large N equivalence with QCD(Adj,-). Similarly, with respect to orbifold planar equivalence, breaking of Z2 interchange symmetry resulting from application of PBC to bifundamental (BF) representation fermions does not invalidate equivalence with QCD(Adj,-) in the one-loop perturbative limit because the partition functions of QCD(BF,-) and QCD(BF,+) are the same. Of particular interest as well is the case of adjoint fermions where for 1$>Nf > 1 Majorana flavour confinement is obtained for sufficiently small m?, and deconfinement for sufficiently large m?. For N ? 3 these two phases are separated by one or more additional phases, some of which can be characterized as partially-confining phases.