Deconfinement on ℝ2×SL1×Sβ1 for all gauge groups and duality to double Coulomb gas
Deconfinement on ℝ2×SL1×Sβ1 for all gauge groups and duality to double Coulomb gas
复制标题
所有规范组的 ℝ2×SL1×Sβ1 解除限制以及双库仑气体的对偶性
DOI：
10.1007/jhep04(2016)109
复制
发表时间：
2016
影响因子：
5.4
通讯作者：
B. Teeple
中科院分区：
文献类型：
--
作者：
B. Teeple
本文研究了在环面R2 × S1 L × S1 β上四维空间中任意规范群G = AN，B，CN，DN，E6，7，8，F4，G2的有限温度N = 1的超杨-米尔斯。特别研究了低温区L（cid：28）β = 1 /T，其中L是空间圆的长度，具有周期边界条件和反周期边界条件，伴随的规范沿着热循环S1 β。对于小这样的L，我们是在一个政权的半经典计算可以进行和过渡发生在Tc远小于1 /NL。跃迁是由非微扰物体之间的竞争介导的，包括“奇异”拓扑分子：由BPS和KK介子组成的中性和磁性玻色子，在规范群G的共根晶格中具有r = rank（G）的不同电荷，以及微扰带电的W玻色子（沿着它们的wino超伙伴）。与非超对称理论的不同之处在于，希格斯沿着热循环产生了一个光模标量场，它与生物子瞬子和W玻色子耦合，并在Tc附近介导了一个跃迁，在那里生物子和W玻色子以相等的强度竞争。这种跃迁类似于在一般规范群下对R3 × S1 L [1，2，12，13]的研究，在一般规范群下对所有群都发现了一阶跃迁，但在SU（2）环R2 × S1 L × S1 β上发现了二阶跃迁，这是在[1]中进行的格点研究.不同电荷的中性和磁性生物子等效二维库仑气体：r m L << r B L/g 2 << d m − m Le 2 π 2 /g 2 << d B − B Le 4 π 2 /g 2，生物子大小，生物子-生物子分离距离和生物子-生物子分离距离。这在弱耦合下成立，表明真空配分函数确实是有效的单极子和双子的2D稀释库仑气体的配分函数。请注意，这个层次在强耦合和库仑气体的“跳跃”中失败了，这表明弱耦合对我们的对偶性的重要性。
: I study finite-temperature N = 1 super Yang-Mills for any gauge group G = A N , B N , C N , D N , E 6 , 7 , 8 , F 4 , G 2 , compactified from four dimensions on a torus, R 2 × S 1 L × S 1 β . I examine in particular the low temperature regime L (cid:28) β = 1 /T , where L is the length of the spatial circle with periodic boundary conditions and with anti-periodic boundary conditions for the adjoint gauginos along the thermal cycle S 1 β . For small such L we are in a regime were semiclassical calculations can be performed and a transition occurs at T c much smaller than 1 /NL . The transition is mediated by the competition between non-perturbative objects including ’exotic’ topological molecules: neutral and magnetic bions composed of BPS and KK monopole constituents, with r = rank ( G ) different charges in the co-root lattice of the gauge group G , and the perturbative electrically charged W-bosons (along with their wino superpartners). The difference from non-SUSY theories here is that the Higgsing along the thermal cycle gives rise to a light modulus scalar field which couples to both bion-instantons and the W-bosons, and mediates a transition near T c where the bions and W-bosons compete with equal strengths. The transition is seen to be similar to previous studies on R 3 × S 1 L [1,2,12,13] with general gauge group where a first order transition was found for all groups, but a second order one for the case of SU (2) on the torus R 2 × S 1 L × S 1 β , which was subjected to lattice studies in [1]. neutral and magnetic bions of different charges effective 2D Coulomb gas: r m ≈ L << r b ≈ L/g 2 << d m − m ≈ Le 2 π 2 /g 2 << d b − b ≈ Le 4 π 2 /g 2 of monopole size, bion size, monopole-monopole separation dis-tance, and bion-bion separation distance. This holds at weak coupling and shows that the vacuum partition function is truly that of an effective 2D dilute Coulomb gas of monopoles and bions. Note that the hierarchy fails at strong coupling and the Coulomb gas ’collapses’, showing the importance of weak coupling to our duality.