The goal of this paper is to present a formalism that allows to handle four-fermion effective theories at finite temperature and density in curved space. The formalism is based on the use of the effective action and zeta function regularization, supports the inclusion of inhomogeneous and anisotropic phases. One of the key points of the method is the use of a non-perturbative ansatz for the heat-kernel that returns the effective action in partially resummed form, providing a way to go beyond the approximations based on the Ginzburg-Landau expansion for the partition function. The effective action for the case of ultra-static Riemannian spacetimes with compact spatial section is discussed in general and a series representation, valid when the chemical potential satisfies a certain constraint, is derived. To see the formalism at work, we consider the case of static Einstein spaces at zero chemical potential. Although in this case we expect inhomogeneous phases to occur only as meta-stable states, the problem is complex enough and allows to illustrate how to implement numerical studies of inhomogeneous phases in curved space. Finally, we extend the formalism to include arbitrary chemical potentials and obtain the analytical continuation of the effective action in curved space.
Renormalization of chiral perturbation theory with spinless matter field in curved spacetime
Institute of Theoretical Physics, Chinese Academy of Sciences（中国科学院理论物理研究所）；School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学学院）
We consider a holographic model of strongly interacting plasma with a gravitational anomaly. In this model, we compute parity-odd responses of the system at finite temperature and chemical potential to external electromagnetic and gravitational fields. Working within the linearized fluid/gravity duality, we performed the calculation up to the third order in gradient expansion. Besides reproducing the chiral magnetic(CME) and vortical (CVE) effects we also obtain gradient corrections to the CME and CVE due to the gravitational anomaly. Additionally, we find energy-momentum and current responses…
We set up a consistent background field formalism for studying the renormalization group (RG) flow of gravity coupled to $N_f$ Dirac fermions on maximally symmetric backgrounds. Based on Wetterich's equation we perform a detailed study of the resulting fixed point structure in a projection including the Einstein-Hilbert action, the fermion anomalous dimension, and a specific coupling of the fermion bilinears to the spacetime curvature. The latter constitutes a mass-type term which breaks chiral symmetry explicitly. Our analysis identifies two infinite families of interacting RG fixed points wh…
In this paper, we shed new light onto $T\bar{T}$-deformations by engineering them on 2D surface defects, supporting chiral and antichiral CFT's, in a 4D Chern-Simons bulk. This approach is motivated by various connections between $T\bar{T}$-deformations, gravity and Chern-Simons theory and suggests that the formalism developed in this paper and the gravity picture of $T\bar{T}$-deformations should be closely related.
In 3+1 dimensional spacetime, two vector gauge anomalies are known: The chiral anomaly and the mixed axial-gravitational anomaly. While the former is well documented and tied to the presence of a magnetic field, the latter instead requires a nonzero spacetime curvature, which has made it rather difficult to study. In this work, we show that a quantum anomaly arises in the second-order electrical response for zero magnetic field, which creates a dc-current that can be either longitudinal or transverse to electric field. Consequently, the continuity equation for the chiral current is not conserv…
Dynamical symmetry breaking in curved spacetime -review-
四费米子相互作用模型被认为是动力学对称性破缺的原型模型，本文综述了四费米子相互作用模型中动力学对称性破缺的研究进展及其在弯曲时空中的推广。从$D$维的Minkowski时空（$2 \leq D \leq 4$）出发，计算了$1/N$展开式首阶的有效势，研究了该理论的相结构.在弯曲时空曲率诱导的相变的费米子质量动态产生的情况下进行了讨论。随后的曲率和温度诱导或曲率和拓扑诱导的相变的可能性进行了讨论。我们还认为，由于引力场的存在，被弱磁场破缺的手征对称性可以恢复。最后简要介绍了四费米子模型在量子引力中的一些应用。
Curved space resolution of singularity of fractional D3-branes on conifold
在三维空间在手征对称性不破缺的$S^3$上紧化的情况下，我们构造了级联$SU(N+M) x SU(N)$超对称规范理论（与Klebanov等人提出的锥上的分数D3膜有关）的超引力对偶. $S^3$的大小可以作为规范理论动力学的红外截止。对于一个足够大的$S^3$，双超重力背景预计是非奇异的。我们证明，这确实是这样的情况下：我们发现一个光滑的IIB型超重力解使用摄动理论是有效的，当半径的$S^3$是大的。我们还考虑了欧几里德世界体积是$S^4$而不是$R x S^3$的情况，在这种情况下，超引力解再次被发现是正则的。分数D3-膜的奇异性在锥解上的这种"弯曲空间“分解类似于我们以前工作中讨论的非极值（有限温度）情况。
The interface between different quantum phases of matter can give rise to novel physics, such as exotic topological phases or non-unitary conformal field theories. Here we investigate the interface between two spin chains in different chiral phases. Surprisingly, the mean-field theory description of this interacting composite system is given in terms of Dirac fermions in a curved space-time geometry. In particular, the boundary between the two phases represents a black hole horizon. We demonstrate that this representation is faithful both analytically, by employing bosonisation to obtain a Lut…
