scholarly journals CASIMIR ENERGY OF 5D ELECTRO-MAGNETISM AND SPHERE LATTICE REGULARIZATION

2008 ◽  
Vol 23 (14n15) ◽  
pp. 2245-2248 ◽  
Author(s):  
SHOICHI ICHINOSE
Keyword(s):  
Renormalization Group ◽  
Closed Form ◽  
Heat Kernel ◽  
Kernel Method ◽  
Casimir Energy ◽  
Closed String ◽  
Extra Space ◽  
Lattice Regularization ◽  
Expanded Form ◽  
Perturbative Treatment

Casimir energy is calculated in the 5D warped system. It is compared with the flat one. The position/ momentum propagator is exploited. A new regularization, called sphere lattice regularization, is introduced. It is a direct realization of the geometrical interpretation of the renormalization group. The regularized configuration is closed-string like. We do not take the KK-expansion approach. Instead the P/M propagator is exploited, combined with the heat-kernel method. All expressions are closed-form (not KK-expanded form). Rigorous quantities are only treated (non-perturbative treatment). The properly regularized form of Casimir energy, is expressed in the closed form. We numerically evaluate its Λ(4D UV-cutoff), ω(5D bulk curvature, warpedness parameter) and T(extra space IR parameter) dependence.

scholarly journals CASIMIR ENERGY OF AdS5 ELECTROMAGNETISM AND COSMOLOGICAL CONSTANT PROBLEM

2009 ◽  
Vol 24 (18n19) ◽  
pp. 3620-3629 ◽  
Author(s):  
S. ICHINOSE
Keyword(s):  
Renormalization Group ◽  
Cosmological Constant ◽  
Casimir Energy ◽  
Cosmological Term ◽  
Geometrical Approach ◽  
Cosmological Constant Problem ◽  
Extra Space ◽  
Lattice Regularization ◽  
Definition Of ◽  
Minimal Area

Casimir energy is calculated for the 5D electromagnetism in the warped geometry. It is compared with the flat case(arXiv:0801.3064). A new regularization, called sphere lattice regularization, is taken. It is based on the minimal area principle and is a direct realization of the geometrical approach to the renormalization group. The properly regularized form of Casimir energy, is expressed in a closed form. We numerically evaluate Λ(4D UV-cutoff), ω(5D bulk curvature, warp parameter) and T(extra space IR parameter) dependence of the Casimir energy. The warp parameter ω suffers from the renormalization effect. We examine the meaning of the weight function and finally reach a new definition of the Casimir energy where the 4D momenta( or coordinates) are quantized with the extra coordinate as the Euclidean time. We comment on the cosmological term at the end.

scholarly journals LATTICE QCD AND STRING THEORY

2006 ◽  
Vol 21 (04) ◽  
pp. 699-706 ◽  
Author(s):  
JULIUS KUTI
Keyword(s):  
String Theory ◽  
Lattice Qcd ◽  
Excitation Spectrum ◽  
Ground State ◽  
Gauge Theories ◽  
Casimir Energy ◽  
Closed String ◽  
Compact Dimension ◽  
Electric Flux ◽  
String Formation

Bosonic string formation in gauge theories is reviewed with particular attention to the confining flux in lattice QCD and its string theory description. Recent results on the Casimir energy of the ground state and the string excitation spectrum are analyzed in the Dirichlet string limit of large separation between static sources. The closed string-soliton (torelon) with electric flux winding around a compact dimension is also discussed.

scholarly journals Normal modes in thermal AdS via the Selberg zeta function

2020 ◽  
Vol 9 (1) ◽  
Author(s):  
Victoria Martin ◽  
Andrew Svesko
Keyword(s):  
Zeta Function ◽  
Heat Kernel ◽  
Normal Mode ◽  
Kernel Method ◽  
Normal Modes ◽  
Quasinormal Mode ◽  
Partition Functions ◽  
Selberg Zeta Function ◽  
Exact Agreement ◽  
Spin Fields

The heat kernel and quasinormal mode methods of computing 1-loop partition functions of spin ss fields on hyperbolic quotient spacetimes \mathbb{H}^{3}/\mathbb{Z}ℍ3/ℤ are related via the Selberg zeta function. We extend that analysis to thermal \text{AdS}_{2n+1}AdS2n+1 backgrounds, with quotient structure \mathbb{H}^{2n+1}/\mathbb{Z}ℍ2n+1/ℤ. Specifically, we demonstrate the zeros of the Selberg function encode the normal mode frequencies of spin fields upon removal of non-square-integrable modes. With this information we construct the 1-loop partition functions for symmetric transverse traceless tensors in terms of the Selberg zeta function and find exact agreement with the heat kernel method.

scholarly journals COSMOLOGICAL CONSTANT PROBING SHAPE MODULI THROUGH LARGE EXTRA DIMENSIONS

2006 ◽  
Vol 21 (15) ◽  
pp. 3095-3109 ◽  
Author(s):  
SATOSHI MATSUDA ◽  
SHIGENORI SEKI
Keyword(s):  
Cosmological Constant ◽  
Extra Dimensions ◽  
Vacuum Energy ◽  
Large Extra Dimensions ◽  
Casimir Energy ◽  
Wilkinson Microwave Anisotropy Probe ◽  
Extra Space ◽  
Kaluza Klein

We consider a compactification of extra dimensions and numerically calculate Casimir energy which is provided by the mass of Kaluza–Klein modes. For the extra space we consider a torus with shape moduli and show that the corresponding vacuum energy is represented as a function of the moduli parameter of the extra dimensions. By assuming that the Casimir energy may be identified with cosmological constant, we evaluate the size of extra dimensions in terms of the recent data given by the Wilkinson Microwave Anisotropy Probe (WMAP) measurement and the supernovae observations. We suggest that the observed cosmological constant may probe the shape moduli of the extra space by the study of the Casimir energy of the compactified extra dimensions.

scholarly journals Closed-form summation of renormalization-group-accessible logarithmic contributions to semileptonicBdecays and other perturbative processes

2002 ◽  
Vol 66 (1) ◽  
Author(s):  
M. R. Ahmady ◽  
F. A. Chishtie ◽  
V. Elias ◽  
A. H. Fariborz ◽  
N. Fattahi ◽  
...  
Keyword(s):  
Renormalization Group ◽  
Closed Form

CHIRAL ANOMALY IN d=4, N=1 SUPERGRAVITY

1995 ◽  
Vol 10 (31) ◽  
pp. 2313-2321 ◽  
Author(s):  
SATOSHI YAJIMA ◽  
YOJI HIGASIDA ◽  
HIDEO TAIRA
Keyword(s):  
Heat Kernel ◽  
Explicit Form ◽  
Kernel Method ◽  
Background Field ◽  
Field Method ◽  
Chiral Anomaly ◽  
Minimal Coupling ◽  
Gravitational Fields ◽  
Background Field Method

The chiral U (1) anomaly in d=4, N=1 supergravity is evaluated on the basis of the heat kernel method. We consider all gravitino interactions of the theory, i.e. not only the minimal coupling of gravitino and gravitational fields, but also four-gravitino interactions which are treated as two-gravitino interactions in the background field method. We show the explicit form of a new contribution from the four-gravitino interactions to the anomaly.

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