The thermal chiral anomaly in the Schwinger model
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Abstract:
In the Schwinger model at finite temperature, we derive a closed form result for the chiral anomaly which arises from the long distance behavior of the electric field \cite{frenkel}. We discuss the general properties associated with this thermal anomaly as well as its relation with the "index" of the Dirac operator. We further show that the thermal anomaly, like the zero temperature anomaly which arises from the ultraviolet behavior of the theory, does not receive any contribution from higher loops. Finally, we determine the complete effective action as well as the anomaly functional on both the thermal branches in the closed time path formalism.Keywords:
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A recently proposed effective action for the trace anomaly describes a tensor-scalar theory that is weakly coupled up to a certain high energy scale, where it becomes strongly interacting. Its ultraviolet completion is obtained by coupling to gravity a quantum field theory in which conformal invariance is spontaneously broken. In this paper, we show that if the field theory that gives rise to the trace anomaly is a large ${N}_{c}$ conformal field theory, then the trace anomaly action has a completion above the strong scale in a holographic Randall-Sundrum two-brane theory, with the radion as a low energy remnant of the spontaneously broken conformal symmetry. Furthermore, we note that the subleading ${N}_{c}$ terms can be derived by adding localized fields to the UV brane, so that the theory remains weakly coupled. The subleading terms are also obtained by introducing the Weyl squared terms in the 5D bulk. These, however, exhibit strongly coupled behavior at the respective sub-Planckian energy scales.
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Chiral anomaly of gamma transition into three pions are studied in a framework of nonlocal chiral quark model. In the local limit the result is in agreement with chiral perturbative theory and reproducesWess-Zumino-Witten anomaly. Transition form factor of gamma into three pions in nonlocal quark model has a correction which vanishes in local limit.
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The Adler-Bell-Jackiw (ABJ) anomaly of a $3+1$ dimensional QED is calculated in the presence of a strong magnetic field. It is shown that in the regime with the lowest Landau level (LLL) dominance a dimensional reduction from $D=4$ to $D=2$ dimensions occurs in the longitudinal sector of the low energy effective field theory. In the chiral limit, the resulting anomaly is therefore comparable with the axial anomaly of a two-dimensional massless Schwinger model. It is further shown that the ${U}_{A}(1)$ anomaly of QED in a strong magnetic field is closely related to the nonplanar axial anomaly of a conventional noncommutative $U(1)$ gauge theory.
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In the Schwinger model at finite temperature, we derive a closed form result for the chiral anomaly which arises from the long distance behavior of the electric field \cite{frenkel}. We discuss the general properties associated with this thermal anomaly as well as its relation with the "index" of the Dirac operator. We further show that the thermal anomaly, like the zero temperature anomaly which arises from the ultraviolet behavior of the theory, does not receive any contribution from higher loops. Finally, we determine the complete effective action as well as the anomaly functional on both the thermal branches in the closed time path formalism.
Anomaly (physics)
Formalism (music)
Conformal anomaly
Operator (biology)
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TRACE (psycholinguistics)
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Using Ads 7 /CFT 6 correspondence we compute a subleading O(N) term in the scale anomaly of (2,0) theory describing N coincident M5 branes. The total scale anomaly extrapolated to N=1 is argued to be the same as the anomaly of a single free (2,0) tensor multiplet. This contribution is based on ref. 1,2 where details and references may be found.
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Conformal anomaly
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