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Register a new userQuantum Tunneling and Back Reaction
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Added by
Bibhas Majhi Ranjan
Publication date
2008
fields
Physics
and research's language is
English
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We give a correction to the tunneling probability by taking into account the back reaction effect to the metric of the black hole spacetime. We then show how this gives rise to the modifications in the semiclassical black hole entropy and Hawking temperature. Finally, we reproduce the familiar logarithmic correction to the Bekenstein-Hawking area law.
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We compute the corrections, using the tunneling formalisim based on a quantum WKB approach, to the Hawking temperature and Bekenstein-Hawking entropy for the Schwarzschild black hole. The results are related to the trace anomaly and are shown to be equivalent to findings inferred from Hawkings original calculation based on path integrals using zeta function regularization. Finally, exploiting the corrected temperature and periodicity arguments we also find the modification to the original Schwarzschild metric which captures the effect of quantum corrections.
We employ gauge-gravity duality to study the backreaction effect of 4-dimensional large-$N$ quantum field theories on constant-curvature backgrounds, and in particular de Sitter space-time. The field theories considered are holographic QFTs, dual to RG flows between UV and IR CFTs. We compute the holographic QFT contribution to the gravitational effective action for 4d Einstein manifold backgrounds. We find that for a given value of the cosmological constant $lambda$, there generically exist two backreacted constant-curvature solutions, as long as $lambda < lambda_{textrm{max}} sim M_p^2 / N^2$, otherwise no such solutions exist. Moreover, the backreaction effect interpolates between that of the UV and IR CFTs. We also find that, at finite cutoff, a holographic theory always reduces the bare cosmological constant, and this is the consequence of thermodynamic properties of the partition function of holographic QFTs on de Sitter.
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 describe in more detail the general relation uncovered in our previous work between boundary correlators in de Sitter (dS) and in Euclidean anti-de Sitter (EAdS) space, at any order in perturbation theory. Assuming the Bunch-Davies vacuum at early times, any given diagram contributing to a boundary correlator in dS can be expressed as a linear combination of Witten diagrams for the corresponding process in EAdS, where the relative coefficients are fixed by consistent on-shell factorisation in dS. These coefficients are given by certain sinusoidal factors which account for the change in coefficient of the contact sub-diagrams from EAdS to dS, which we argue encode (perturbative) unitary time evolution in dS. dS boundary correlators with Bunch-Davies initial conditions thus perturbatively have the same singularity structure as their Euclidean AdS counterparts and the identities between them allow to directly import the wealth of techniques, results and understanding from AdS to dS. This includes the Conformal Partial Wave expansion and, by going from single-valued Witten diagrams in EAdS to Lorentzian AdS, the Froissart-Gribov inversion formula. We give a few (among the many possible) applications both at tree and loop level. Such identities between boundary correlators in dS and EAdS are made manifest by the Mellin-Barnes representation of boundary correlators, which we point out is a useful tool in its own right as the analogue of the Fourier transform for the dilatation group. The Mellin-Barnes representation in particular makes manifest factorisation and dispersion formulas for bulk-to-bulk propagators in (EA)dS, which imply Cutkosky cutting rules and dispersion formulas for boundary correlators in (EA)dS. Our results are completely general and in particular apply to any interaction of (integer) spinning fields.
We investigate flux vacua on a variety of one-parameter Calabi-Yau compactifications, and find many examples that are connected through continuous monodromy transformations. For these, we undertake a detailed analysis of the tunneling dynamics and find that tunneling trajectories typically graze the conifold point---particular 3-cycles are forced to contract during such vacuum transitions. Physically, these transitions arise from the competing effects of minimizing the energy for brane nucleation (facilitating a change in flux), versus the energy cost associated with dynamical changes in the periods of certain Calabi-Yau 3-cycles. We find that tunneling only occurs when warping due to back-reaction from the flux through the shrinking cycle is properly taken into account.
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