Modern Physics Letters A

The two surprising features of gravity are (a) the principle of equivalence and (b) the connection between gravity and thermodynamics. Using principle of equivalence and special relativity in the local inertial frame, one could obtain the insight that gravity must possess a geometrical description. We show that, using the same principle of equivalence, special relativity and quantum theory in the local Rindler frame one can obtain the Einstein–Hilbert action functional for gravity and thus the dynamics of the space–time. This approach, which essentially involves postulating that the horizon area must be proportional to the entropy, uses the local Rindler frame as a natural extension of the local inertial frame and leads to the interpretation that the gravitational action represents the free energy of the space–time geometry. As an aside, one also obtains a natural explanation as to: (i) why the covariant action for gravity contains second derivatives of the metric tensor and (ii) why the gravitational coupling constant is positive. The analysis suggests that gravity is intrinsically holographic and even intrinsically quantum mechanical.

We obtain the energy distribution of the gamma metric using the energy–momentum complex of Møller. The result is the same as that obtained by Virbhadra in the Weinberg prescription.

We consider in detail how the quantum-mechanical tunneling phenomenon occurs in a well-behaved octic potential. Our main tool will be the Euclidean propagator just evaluated between two minima of the potential at issue. For such a purpose we resort to the standard semiclassical approximation which takes into account the fluctuations over the instantons, i.e. the finite-action solutions of the Euclidean equation of motion. With respect to the one-instanton approach, the functional determinant associated with the so-called stability equation is analyzed in terms of the asymptotic behavior of the zero-mode. The conventional ratio of determinants takes as reference the harmonic oscillator whose frequency is the average of the two different frequencies derived from the minima of the potential involved in the computation. The second instanton of the model is studied in a similar way. The physical effects of the multi-instanton configurations are included in this context by means of the alternate dilute-gas approximation where the two instantons participate to give the final expression of the propagator.

We give a simplified and more complete description of the loop variable approach for writing down gauge-invariant equations of motion for the fields of the open string. A simple proof of gauge invariance to all orders is given. In terms of loop variables, the interacting equations look exactly like the free equations, but with a loop variable depending on an extra parameter, thus making it a band of finite width. The arguments for gauge invariance work exactly as in the free case. We show that these equations are Wilsonian RG equations with a finite worldsheet cutoff and that in the ir limit, equivalence with the Callan–Symanzik β-functions should ensure that they reproduce the on-shell scattering amplitudes in string theory. It is applied to the tachyon–photon system and the general arguments for gauge invariance can be easily checked to the order calculated. One can see that when there is a finite worldsheet cutoff in place, even the U(1) invariance of the equations for the photon, involves massive mode contributions. A field redefinition involving the tachyon is required to get the gauge transformations of the photon into the standard form.

Exact renormalization group techniques are applied to the mass deformed super-symmetric Yang–Mills theory, viewed as a regularized model. The solution of the flow equation, in case of dominance of the potential term, reproduces the one-loop (perturbatively exact) expression for the effective action of supersymmetric Yang–Mills theory, when the regularizing mass, M, reaches the value of the dynamical cutoff Λ. One speculates about the way in which further nonperturbative contributions (instanton effects) may be accounted for.

Gravitational field of cosmic strings in theories with extra spatial dimensions differs significantly from that in the 4D Einstein's theory. This means that all gravity induced properties of cosmic strings need to be revised. Here we consider the effect of vacuum polarization outside a straight infinitely thin cosmic string embedded in RS2 brane world.