Romatschke Paul
Department of Physics, University of Colorado, Boulder, Colorado 80309, USA and Center for Theory of Quantum Matter, University of Colorado, Boulder, Colorado 80309, USA.
Phys Rev Lett. 2019 Jun 14;122(23):231603. doi: 10.1103/PhysRevLett.122.231603.
A famous example of gauge-gravity duality is the result that the entropy density of the strongly coupled N=4 supersymmetric Yang-Mills theory in four dimensions for large N is exactly 3/4 of the Stefan-Boltzmann limit. In this work, I revisit the massless O(N) model in 2+1 dimensions, which is analytically solvable at a finite-temperature T for all couplings λ in the large N limit. I find that the entropy density monotonically decreases from the Stefan-Boltzmann limit at λ=0 to exactly 4/5 of the Stefan-Boltzmann limit at λ=∞. Calculating the retarded energy-momentum tensor correlator in the scalar channel at λ=∞, I find that it has two logarithmic branch cuts originating at ω=±4Tln(1+sqrt[5]/2) but no singularities in the whole complex frequency plane. I show that the ratio 4/5 and the location of the branch points both are universal within a large class of bosonic conformal field theories in 2+1 dimensions.
规范-引力对偶的一个著名例子是这样一个结果：对于大N的四维强耦合N = 4超对称杨-米尔斯理论，其熵密度恰好是斯特藩-玻尔兹曼极限的3/4。在这项工作中，我重新审视了2 + 1维的无质量O(N)模型，该模型在大N极限下对于所有耦合常数λ在有限温度T时是可解析求解的。我发现熵密度从λ = 0时的斯特藩-玻尔兹曼极限单调下降到λ = ∞时恰好是斯特藩-玻尔兹曼极限的4/5。在λ = ∞时标量通道中计算推迟能量-动量张量关联函数，我发现它有两个源于ω = ±4Tln(1 + √5/2)的对数分支割线，但在整个复频率平面上没有奇点。我表明4/5这个比值以及分支点的位置在2 + 1维的一大类玻色共形场论中都是普适的。
