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Register a new userHolographic Schwinger Effect and Chiral condensate in SYM Theory
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We study the instability, for the supersymmetric Yang-Mills (SYM) theories, caused by the external electric field through the imaginary part of the action of the D7 probe brane, which is embedded in the background of type IIB theory. This instability is related to the Schwinger effect, namely to the quark pair production due to the external electric field, for the $SU(N_c)$ SYM theories. In this holographic approach, it is possible to calculate the Schwinger effect for various phases of the theories. Here we give the calculation for ${cal N}=2$ SYM theory and the analysis is extended to the finite temperature deconfinement and the zero temperature confinement phases of the Yang-Mills (YM) theory. By comparing the obtained production rates with the one of the supersymmetric case, the dynamical quark mass is estimated and we find how it varies with the chiral condensate. Based on this analysis, we give a speculation on the extension of the Nambu-Jona-Lasinio model to the finite temperature YM theory, and four fermi coupling is evaluated in the confinement theory.
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We consider the theory of Rarita-Schwinger field interacting with a field with spin 1/2, in the case of finite temperature, chemical potential and vorticity, and calculate the chiral vortical effect for spin 3/2. We have clearly demonstrated the role of interaction with the spin 1/2 field, the contribution of the terms with which to CVE is 6. Since the contribution from the Rarita-Schwinger field is -1, the overall coefficient in CVE is 6-1=5, which corresponds to the recent prediction of a gauge chiral anomaly for spin 3/2. The obtained values for the coefficients $mu^2$ and $T^2$ are proportional to each other, but not proportional to the spin, which indicates a possible new universality between the temperature-related and the chemical potential-related vortical effects. The results obtained allow us to speculate about the relationship between the gauge and gravitational chiral anomalies.
A holographic bottom-up model used in studying the superconducting system is applied to search for the color superconducting phase of supersymmetric Yang-Mills theory. We apply the probe analysis of this model to the supersymmetric Yang-Mills theory in both the confinement and deconfinement phases. In this analysis, we find the color superconductivity in both phases when the baryon chemical potential exceeds a certain critical value. This result implies that, above the critical chemical potential, a color non-singlet diquark operator, namely the Cooper pair, has its vacuum expectation value even in the confinement phase. In order to improve this peculiar situation, we proceed the analysis by taking account of the full back-reaction from the probe. As a result, the color superconducting phase, which is observed in the probe approximation, disappears in both the confinement and deconfinement phases when parameters of the theory are set within their reasonable values.
We study the time evolution of early universe which is developed by a cosmological constant $Lambda_4$ and supersymmetric Yang-Mills (SYM) fields in the Friedmann-Robertson-Walker (FRW) space-time. The renormalized vacuum expectation value of energy-momentum tensor of the SYM theory is obtained in a holographic way. It includes a radiation of the SYM field, parametrized as $C$. The evolution is controlled by this radiation $C$ and the cosmological constant $Lambda_4$. For positive $Lambda_4$, an inflationary solution is obtained at late time. When $C$ is added, the quantum mechanical situation at early time is fairly changed. Here we perform the early time analysis in terms of two different approaches, (i) the Wheeler-DeWitt equation and (ii) Lorentzian path-integral with the Picard-Lefschetz method by introducing an effective action. The results of two methods are compared.
We study the time development of strongly coupled ${cal N}=4$ supersymmetric Yang Mills (SYM) theory on cosmological Friedmann-Robertson-Walker (FRW) backgrounds via the AdS/CFT correspondence. We implement the cosmological background as a boundary metric fulfilling the Friedmann equation with a four-dimensional cosmological constant and a dark radiation term. We analyze the dual bulk solution of the type IIB supergravity and find that the time-dependence of the FRW background strongly influences the dynamical properties of the SYM theory. We in particular find a phase transition between a confined and a deconfined phase. We also argue that some cosmological solutions could be related to the inflationary scenario.
The Schwinger effect in the presence of instantons is considered in this paper. Using AdS/CFT correspondence in the near horizon limit of the D3+D($-1$)-brane background, we calculate the total potential of a quark-antiquark pair in an external electric field. It is shown that instantons tend to suppress the pair creation effect and increase the critical electric field above which the pairs are produced freely without any suppression. Interestingly, no other critical electric field, common for all confining field theories, is observed here at finite temperature. However, as expected we find such a critical electric field at zero temperature. The pair production rate evaluated by the calculation of the expectation value of the circular Wilson loop also confirms this result.
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