We present two new results on relativistic hydrodynamics with anomalies and external electromagnetic fields, "Chiral MagnetoHydroDynamics" (CMHD). First, we study CMHD in four dimensions at second order in the derivative expansion assuming the conformal/Weyl invariance. We classify all possible independent conformal second order viscous corrections to the energy-momentum tensor and to the U(1) current in the presence of external electric and/or magnetic fields, and identify eighteen terms that originate from the triangle anomaly. We then propose and motivate the following guiding principle to constrain the CMHD: the anomaly--induced terms that are even under the time reversal invariance should not contribute to the local entropy production rate. This allows us to fix thirteen out of the eighteen transport coefficients that enter the second order formulation of CMHD. We also relate one of our second order transport coefficients to the chiral shear waves. Our second subject is hydrodynamics with (N+1)-gon anomaly in an arbitrary 2N dimensions. The effects from the (N+1)-gon anomaly appear in hydrodynamics at (N-1)'th order in the derivative expansion, and we identify precisely N such corrections to the U(1) current. The time reversal constraint is powerful enough to allow us to find the analytic expressions for all transport coefficients. We confirm the validity of our results (and of the proposed guiding principle) by an explicit fluid/gravity computation within the AdS/CFT correspondence.
We revisit the question of time reversal and $CP$ invariance in Calabi-Yau compactifications. We show that time reversal invariance is respected by quantum corrections to the prepotential. In particular, field independent $θ$ angles whose presence is dictated by requiring integrality of relevant monodromy transformations can take precisely the quantized values compatible with time reversal invariance. Furthermore, monodromy symmetry enlarges the region on moduli space on which time reversal is not spontaneously broken. We define the action of the $CP$ transformation for multi-parameter models …
The generalization of scale invariance when gravitational effects are considered is Weyl invariance, namely, invariance under (global or local) rescalings of the metric. In this work, we discuss in some details the implications of the fact that the value of the anomaly for the global Weyl invariant coupling of scalar fields to gravity is sensitive to the dynamics (or absence thereof) of the gravitational field.
We study a series of the Wess-Zumino actions obtained by repeatedly integrating conformal anomalies with respect to the conformal-factor field that appear at higher loops. We show that they arise as physical quantities required to make nonlocal loop correction terms diffeomorphism invariant. Specifically, in a conformally flat spacetime $ds^2=e^{2ϕ}(-dη^2 + d{\bf x}^2)$, we find that effective actions are described in terms of momentum squared expressed as a physical $Q^2 = q^2/e^{2ϕ}$ for $q^2$ measured by the flat metric, which recalls the relationship between physical momentum and comoving …
't Hooft anomaly matching is powerful for constraining the low energy phases of gauge theories. In 3d one common anomaly is the parity anomaly in a $T$-symmetric theory where one cannot gauge the global symmetry group without breaking the time-reversal symmetry. We find that a $T$-symmetric $\text{SU}(N)$ gauge theory with either fermionic or bosonic matter in the fundamental representation of the gauge group has a parity anomaly between the flavor group and $T$-symmetry provided that there is also a massless Majorana fermion in the adjoint representation of the gauge group. We then analyze th…
A Pedagogical Introduction to Anomalies in Quantum Field Theory
Laboratoire de Physique de l’École Normale Supérieure PSL University, CNRS, Sorbonne Université, Université Paris Cité（巴黎高等师范学院物理实验室、PSL大学、法国国家科学研究中心、索邦大学、巴黎西岱大学）
It is known that the elimination of the anomalies in all orders of perturbation theory is an open problem. The constrains given by usual invariance properties and the Wess-Zumino identities are not enough to eliminate the anomalies in the general case of an Yang-Mills theory. So, any new symmetry of the model could restrict further the anomalies and be a solution of the problem. We consider the anti-BRST transform of Ojima in the causal approach and investigate if such new restrictions are obtained. Unfortunately, the result is negative: if we have BRST invariance up to the second order of the…
Usually, in order to compute an anomaly (be it chiral or trace) with a perturbative method, the lowest significant order is sufficient. With the help of gauge or diffeomorphism invariance it uniquely identifies the anomaly. This note is a short review of the ambiguities that arise in the calculation of trace anomalies, and is meant, in particular, to signal cases in which the lowest perturbative order is not enough to unambiguously identify a trace anomaly. This may shed light on some recent contradictory results.
We explore 4d Yang-Mills gauge theories (YM) living as boundary conditions of 5d gapped short/long-range entangled (SRE/LRE) topological states. Specifically, we explore 4d time-reversal symmetric pure YM of an SU(2) gauge group with a second-Chern-class topological term at $θ=π$ (SU(2)$_{θ=π}$ YM), by turning on background fields for both the time-reversal (i.e., on unorientable manifolds) and 1-form center global symmetry. We find four classes of time-reversal and Lorentz symmetry-enriched SU(2)$_{θ=π}$ YM, labeled by $(K_1, K_2)$: $K_1=0,1$ specifies Kramers singlet/doublet Wilson line and …
