We elucidate chirality production under parity breaking constant electromagnetic fields, with which we clarify qualitative differences in and out of equilibrium. For a strong magnetic field the pair production from the Schwinger mechanism increments the chirality. The pair production rate is exponentially suppressed with mass according to the Schwinger formula, while the mass dependence of chirality production in the axial Ward identity appears in the pesudo-scalar term. We demonstrate that in equilibrium field theory calculus the axial anomaly is canceled by the pseudo-scalar condensate for any mass. In a real-time formulation with in- and out-states, we show that the axial Ward identity leads to the chirality production rate consistent with the Schwinger formula. We illuminate that such an in- and out-states formulation makes clear the chiral magnetic effect in and out of equilibrium, and we discuss further applications to real-time condensates.
The anomalous generation of chirality with mass effects via the axial Ward identity and its dependence on the Schwinger mechanism is reviewed, utilizing parity violating homogeneous electromagnetic background fields. The role vacuum asymptotic states play on the interpretation of expectation values is examined. It is discussed that observables calculated with an in-out scattering matrix element predict a scenario under Euclidean equilibrium. A notable ramification of which is a vanishing of the chiral anomaly. In contrast, it is discussed observables calculated under an in-in, or real-time, fo…
Building on our recent derivation of the Ward-Schwinger-Dyson equations for the cubic interaction model, we present here the first steps of their resurgent analysis. In our derivation of the WSD equations, we made sure that they had the properties of compatibility with the renormalisation group equations and independence from a regularisation procedure which was known to allow for the comparable studies in the Wess-Zumino model. The interactions between the transseries terms for the anomalous dimensions of the field and the vertex is at the origin of unexpected features, for which the effect o…
We develop a system of equations for the propagators and three point functions of the $ϕ^3$ quantum field theory in six dimensions. Inspired from a refinement by Ward on the Schwinger--Dyson equations, the main characteristics of this system are to be formulated purely in terms of renormalized quantities and to give solutions satisfying renormalisation group equations. These properties were difficult to get together, due to the overlapping divergences in the propagator. The renormalisation group equations are an integral part of any efficient resolution scheme of this system and will be instru…
In QCD, the Schwinger mechanism endows the gluons with an effective mass through the dynamical formation of massless bound-state poles that are longitudinally coupled. The presence of these poles affects profoundly the infrared properties of the interaction vertices, inducing crucial modifications to their fundamental Ward identities. Within this general framework, we present a detailed derivation of the non-Abelian Ward identity obeyed by the pole-free part of the three-gluon vertex in the soft-gluon limit, and determine the smoking-gun displacement that the onset of the Schwinger mechanism p…
Bodeker's Effective Theory: From Langevin Dynamics to Dyson-Schwinger Equations
如果特征动量标度为|k| ~ g ^2 T，则高温下弱耦合非阿贝尔规范场的动力学是非微扰的。这种情况在早期宇宙的电弱重子数破坏过程中是典型的。博德克推导了一个有效的理论，该理论通过朗之万方程描述了软场模式的动力学。这种有效的理论已被用于晶格计算到目前为止。在这项工作中，我们提供了一个互补的，更多的分析方法的基础上戴森Schwinger方程。使用已知的随机量子化的方法，我们重铸博德克的朗之万方程的形式的场论路径积分。我们引入规范鬼，以帮助控制可能出现的规文物截断后，这导致了BRST对称制定和相应的沃德恒等式。第二套沃德恒等式，反映了起源的理论在随机微分方程，也得到。最后导出了Dyson-Schwinger方程。
In this work, we show that Lorentz invariant theories in $1+1$ dimensions admit new terms inspired by Very Special Relativity (VSR) theories. We have studied the Schwinger model in VSR. We show the axial current is classically conserved in the presence of a mass term coming from the VSR invariant terms but without standard Lorentz invariant mass. Furthermore, it is shown that both the vector current as well as the axial current are modified with respect to the free case when the fermion is coupled to an external electromagnetic field due to the nonlocal operator present in the theory. The axia…
We study the discrete chiral- and center-symmetry 't Hooft anomaly matching in the charge-$q$ two-dimensional Schwinger model. We show that the algebra of the discrete symmetry operators involves a central extension, implying the existence of $q$ vacua, and that the chiral and center symmetries are spontaneously broken. We then argue that an axial version of the $q$$=$$2$ model appears in the worldvolume theory on domain walls between center-symmetry breaking vacua in the high-temperature $SU(2)$ ${\cal N}$$=$$1$ super-Yang-Mills theory and that it inherits the discrete 't Hooft anomalies of t…
We study conformal Ward-Takahashi identities for two-point functions in $d(\geq3)$-dimensional finite-temperature conformal field theory. We first show that the conformal Ward-Takahashi identities can be translated into the intertwining relations of conformal algebra $\mathfrak{so}(2,d)$. We then show that, at finite temperature, the intertwining relations can be translated into the recurrence relations for two-point functions in complex momentum space. By solving these recurrence relations, we find the momentum-space two-point functions that satisfy the Kubo-Martin-Schwinger thermal equilibri…
We treat random rank-$D$ tensor models as $D$-dimensional quantum field theories---tensor field theories (TFT)---and review some of their non-perturbative methods. We classify the correlation functions of complex tensor field theories by boundary graphs, sketch the derivation of the Ward-Takahashi identity and stress its relevance in the derivation of the tower of exact, analytic Schwinger-Dyson equations for all the correlation functions (with connected boundary) of TFTs with quartic pillow-like interactions.
We analyse in this paper the large N limit of the Schwinger-Dyson equations in a rank-3 tensor quantum field theory, which are derived with the help of Ward-Takahashi identities. In order to have a well-defined large N limit, appropriate scalings in powers of N for the various terms present in the action are explicitly found. A perturbative check of our results is done, up to second order in the coupling constant.
We study symmetries of quantum field theories involving topologically distinct sectors of the field space. To exhibit these symmetries we define special gauge invariant observables, which we call the $qq$-characters. In the context of the BPS/CFT correspondence, using these observables, we derive an infinite set of Dyson-Schwinger-type relations. These relations imply that the supersymmetric partition functions in the presence of $Ω$-deformation and defects obey the Ward identities of two dimensional conformal field theory and its $q$-deformations. The details will be discussed in the companio…
We study a special Schwinger-Dyson equation in the context of a pure SU(3) Yang-Mills theory, formulated in the background field method. Specifically, we consider the corresponding equation for the vertex that governs the interaction of two background gluons with a ghost-antighost pair. By virtue of the background gauge invariance, this vertex satisfies a naive Slavnov-Taylor identity, which is not deformed by the ghost sector of the theory. In the all-soft limit, where all momenta vanish, the form of this vertex may be obtained exactly from the corresponding Ward identity. This special result…
Augmentations to the Euler-Heisenberg Lagrangian (QED one-loop effective action in homogeneous electromagnetic fields) under a constant background axial gauge are examined. Two special configurations admit an exact eigendecomposition, and hence effective action as a spectral sum, of the augmented Dirac operator: one with a magnetic field with chiral chemical potential, and the other with an electric field with spatial axial gauge, which resembles an emergent vorticity. An enhancement to Schwinger pair production is found for the latter, which is more fully analyzed using the worldline instanto…
We argue that the topological charge of nonabelian gauge theory is unphysical. To show this statement, we use the Adler-Bardeen theorem and the Becchi-Rouet-Stora-Tyutin symmetry which are warranted by the perturbative finiteness of the chiral anomaly, thus being free of Gribov ambiguity. In addition to the original argument using the unphysical gauge field component collinear to the spatial derivative of the gauge function, we show the unobservability of the topological charge using the Ward-Takahashi identity. We then present the consequences of this finding and show the consistency with man…
It is known that soft photon and graviton theorems can be regarded as the Ward-Takahashi identities of asymptotic symmetries. In this paper, we consider soft theorem for pions, i.e., Nambu-Goldstone bosons associated with a spontaneously broken axial symmetry. The soft pion theorem is written as the Ward-Takahashi identities of the $S$-matrix under asymptotic transformations. We investigate the asymptotic dynamics, and find that the conservation of charges generating the asymptotic transformations can be interpreted as a pion memory effect.
