arXiv 0712.26862007-12-17hep-th

Comment on "Remark on the renormalization group equation for the Penner model"

Noureddine Chair

备注：: 4 pages
发表信息：: Phys.Rev.D75:127901,2007
DOI：: 10.1103/PhysRevD.75.127901

英文摘要：

We show explicitly that the sum over punctures for the three times derivative for the Penner free energy $F_{0}^{3}$, given by D.A. Johnston, Phys.Rev.D 51 (1995) is not correct. As a consequence, Eq.(21), the differentiated version for the renormalization group (RG) equation, is wrong. Also, his conclusion that the differentiated version of the (RG) equation for the three-times derivative of the free energy can be obtained from the higher genus (RG) equation can not be true. Finally, the differentiated version of the (RG) equation is extended to any $s$ derivative of the free energy $F_{0}$.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

阅读原文

阅读 PDF ↗

arXiv 页面 ↗HTML 原文 ↗

本文内容

英文摘要相关论文

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

继续探索

相关论文

A Remark on the Renormalization Group Equation for the Penner Model

It is possible to extract values for critical couplings and gamma_string in matrix models by deriving a renormalization group equation for the variation of the of the free energy as the size N of the matrices in the theory is varied. In this paper we derive a ``renormalization group equation'' for the Penner model by direct differentiation of the partition function and show that it reproduces the correct values of the critical coupling and gamma_string and is consistent with the logarithmic corrections present for g=0,1.

1994-06-21hep-th

Some Remarks About the Two-Matrix Penner Model and the Kazakov-Migdal Model

I consider the Hermitean two-matrix model with a logarithmic potential which is associated in the one-matrix case with the Penner model. Using loop equations I find an explicit solution of the model at large N (or in the spherical approximation) and demonstrate that it solves the corresponding Riemann-Hilbert problem. I construct the potential of the Kazakov-Migdal model on a D-dimensional lattice, which turns out to be a sum of two logarithms as well, whose large-N solution is given by the same formulas. In the "naive" continuum limit this potential recovers in D<4 dimensions the standard sca…

1993-06-08hep-th

Remark to the Comment on "New pseudoclassical model for Weyl particles"

We present here our considerations concerning the problem of classical consistency of pseudoclassical models touched upon in a recent comment on our paper "New pseudoclassical model for Weyl particle".

1996-02-27hep-th

Technical Remarks and Comments on the UV/IR-Mixing Problem of a Noncommutative Scalar Quantum Field Theory

In this letter we will dicuss the possibility of a resummation procedure in order to cure the UV/IR-mixing problem of noncommutative field theories. The method is presented for a scalar phi^4 theory on Euclidean space. Finally, we sketch the idea of resummation for U(1)-gauge theories.

2003-02-06hep-th

Comments on Gauged WZW Models

Some remarks are made about free anomaly groups in gauged WZW models. Considering a quite general action, anomaly cancellation is analyzed. The possibility of gauging left and right sectors independently in some cases is remarked. In particular Toda theories can be seen as such a kind of models.

1992-01-31hep-th

More comments on the high-energy behavior of string scattering amplitudes in warped spacetimes

We study the Regge limit of string amplitudes within the model of Polchinski-Strassler for string scattering in warped spacetimes. We also present some numerical estimations of the Regge slopes. It is quite remarkable that the real values of the slopes are inside a range of ours.

2005-12-21hep-th

更多相关论文收起更多论文

Remarks on spherical monodromy defects for free scalar fields

The computation of the effect of a simple monodromy defect in the case of a sphere with twisted boundary conditions is revisited and streamlined using earlier calculations for a similar system. Compact and explicit expressions are found for arbitrary integer dimensions. Comments on other work are made.

2021-04-26hep-th

Some remarks about intrinsic parity in Ryder's derivation of the Dirac equation

This work is a comment on Ryder's derivation of the Dirac equation, with emphasis on the physical contents of this equation: the notion of particles and antiparticles according to the Stueckelberg-Feynman interpretation, the opposite intrinsic parity between particles and antiparticles, and the spin.

1998-07-28hep-th

Comments on open string with "massive" boundary term

We make some remarks on possible definition of open string path integral in the presence of additional boundary couplings corresponding to the presence of masses at the ends of the string. These couplings are not conformally invariant implying that as in a non-critical string case one is to integrate over the 1d metric or reparametrizations of the boundary. We compute the partition function on the disc in the presence of an additional constant gauge field background and comment on the structure of the corresponding scattering amplitudes.

2020-11-11hep-th

Comments on knotted 1/2 BPS Wilson loops

In this paper, we show that the localization of three-dimensional N = 2 supersymmetric Chern-Simons theory on the ellipsoid-like squashed sphere is related to a nontrivial knot structure called torus knot. More precisely, we can capture the three sphere as the nontrivial so-called Seifert fibrations by regarding 1/2 BPS Wilson loops as U(1) fibers. The topology of knotted 1/2 BPS Wilson loops is controlled by squashing parameters. We calculate the 1/2 BPS condition of the Wilson loop and find perfect agreement with known results. We also remark on the level shift and framing anomaly.

2013-12-24hep-th

Comment on `One Loop Renormalization of Soliton Quantum Mass Corrections in 1+1 Dimensional Scalar Field Theory Models' (Phys. Lett. B542 (2002) 282 [hep-th/0206047])

We refute the claim that previous works on the one-loop quantum mass of solitons had incorrectly dropped a surface term from a partial integration. Rather, the paper quoted in the title contains a fallacious derivation with two compensating errors. We also remark that the $ϕ^2\cos^2\ln(ϕ^2)$ model considered in that paper does not have solitons at the quantum level because at two-loop order the degeneracy of the vacua is lifted. This may be remedied, however, by a supersymmetric extension.

2002-11-18hep-th

Comment on "Casimir effect in a weak gravitational field: Schwinger's approach"

We show that the statement in F. Sorge [Class. Quant. Grav. 36, no.23, 235006 (2019)] that the Casimir effect receives second order corrections due to gravity is not consistent. We remark especially on the tracing of the proper time Hamiltonian, where the correct procedure is to use the eigenfunctions and eigenvalues of the covariant DAlembertian. After some cancellations we find that the value of the functional W [0] is the same as obtained by Sorge. However, we argue that the proper vacuum energy density carries extra space-time volume terms that cancel over the gravitational correction, ret…

2020-08-13hep-th

Comments on the Riemann conjecture and index theory on Cantorian fractal space-time

An heuristic proof of the Riemman conjecture is proposed. It is based on the old idea of Polya-Hilbert. A discrete/fractal derivative self adjoint operator whose spectrum may contain the nontrivial zeroes of the zeta function is presented. To substantiate this heuristic proposal we show using generalized index-theory arguments, corresponding to the (fractal) spectral dimensions of fractal branes living in Cantorian-fractal space-time, how the required $negative$ traces associated with those derivative operators naturally agree with the zeta function evaluated at the spectral dimensions. The $ζ…

2001-04-08hep-th

On Remarks on the spin-one Duffin-Kemmer-Petiau equation in the presence of nonminimal vector interactions in (3+1) dimensions

In a very recent manuscript [arXiv:1403.6035], Castro and Oliveira have commented on our recently published paper [2]. Their main criticism is that we have used an improper nonminimal interaction term. Regarding their work, we wish to mention two points. 1. We have started the paper based on the work of Kozak et al. [3] which has successfully discussed the deuteron-nucleus scattering. 2. The second point is that we have used in our calculations \b{eta}0 and not (which preserves the current conservation). Therefore, the content of our work is correct.

2014-04-17hep-th

Comments on Exact Quantization Conditions and Non-Perturbative Topological Strings

We give some remarks on exact quantization conditions associated with quantized mirror curves of local Calabi-Yau threefolds, conjectured in arXiv:1410.3382. It is shown that they characterize a non-perturbative completion of the refined topological strings in the Nekrasov-Shatashvili limit. We find that the quantization conditions enjoy an exact S-dual invariance. We also discuss Borel summability of the semi-classical spectrum.

2015-09-07hep-thmath-phmath.MP

Some Remarks on Theories with Large Compact Dimensions and TeV-Scale Quantum Gravity

We comment on some implications of theories with large compactification radii and TeV-scale quantum gravity. These include the behavior of high-energy gravitational scattering cross sections and consequences for ultra-high-energy cosmic rays and neutrino scattering, the question of how to generate naturally light neutrino masses, the issue of quark-lepton unification, the equivalence principle, and the cosmological constant.

1998-11-13hep-phhep-th

The Legacy of M. P. Bronstein: on relativistic wave equations for spin 2 fields and some comments

We briefly give a very simple picture about one of the most remarkable results of Matvej Petrovich Bronstein concerning the quantization of the gravitational waves showing also that the linearized Einstein equations of the paper: Phys.Rev. D65 (2002) 104005 are the same Bronstein's equations given 66 years before.

2014-10-23gr-qchep-thphysics.hist-ph