THE VILKOVISKY EFFECTIVE ACTION IN THE EVEN-DIMENSIONAL QUANTUM GRAVITY

1989 ◽  
Vol 04 (07) ◽  
pp. 633-644 ◽  
Author(s):  
I. L. BUCHBINDER ◽  
E. N. KIRILLOVA ◽  
S. D. ODINTSOV
Keyword(s):  
Numerical Calculation ◽  
Effective Potential ◽  
Effective Action ◽  
Equations Of Motion ◽  
Flat Space ◽  
Einstein Gravity ◽  
Quantum Field ◽  
Dimensional Torus ◽  
Spontaneous Compactification ◽  
The One

The one-loop Vilkovisky effective potential which is not dependent on a gauge and a parametrization of quantum field, is investigated. We have considered Einstein gravity on a background manifold of (flat space) × (d−4- sphere) or × (d−4- dimensional torus ), d is even, and of R3 × (1- sphere ), where R3 is flat space. The numerical calculation for the cases R4 × Td−4 (d = 6,8,10) and R3 × S1 is done. The solution to the one-loop corrected equations of motion is found, although the spontaneous compactification is not stable in these cases.

EFFECTIVE ACTION IN MULTI-DIMENSIONAL SUPERGRAVITIES AND INDUCED EINSTEIN GRAVITY

1988 ◽  
Vol 03 (08) ◽  
pp. 1859-1870 ◽  
Author(s):  
I.L. BUCHBINDER ◽  
S.D. ODINTSOV
Keyword(s):  
Boundary Conditions ◽  
General Expression ◽  
Effective Action ◽  
Einstein Gravity ◽  
Space Time ◽  
Dimensional Torus ◽  
Curved Space ◽  
Dimensional Gravity ◽  
The One

In the present paper a general expression of quantum effective action for arbitrary d-dimensional supergravity on the background Rn×Td−n′ where Rn is n-dimensional curved space-time, Td is d-dimensional torus, is obtained as an expansion on the curvature and its derivatives. The mechanism of inducing Einstein gravity with zero Λ term is proposed. It is shown that the 4-dimensional gravity with the true sign of the Newton constant is induced from d=5 supergravity when antiperiodic boundary conditions are chosen for all fields of supermultiplet. The one-loop effective action is obtained for d=4, 5, 7, 10 supergravities with the accuracy of linear curvature terms. The one-loop Vilcovisky-De Witt effective action is also obtained for d=5 SG’s with the accuracy of linear curvature terms.

SPONTANEOUS SUPERSYMMETRY BREAKING AND EFFECTIVE ACTION IN SUPERSYMMETRICAL KALUZA-KLEIN THEORIES AND STRINGS

1989 ◽  
Vol 04 (17) ◽  
pp. 4337-4351 ◽  
Author(s):  
I. L. BUCHBINDER ◽  
S. D. ODINTSOV
Keyword(s):  
Minkowski Space ◽  
Supersymmetry Breaking ◽  
Effective Action ◽  
Vacuum Energy ◽  
Nonzero Temperature ◽  
Dimensional Torus ◽  
Spontaneous Compactification ◽  
Curved Space ◽  
The One ◽  
Kaluza Klein

The one-loop effective action (EA) for arbitrary supersymmetric theory with broken supersymmetry on the background Rb × Td−n, where Rn, Td are n-dimensional curved space-time and d-dimensional torus, is obtained. Vilcovisky-De Witt EA in d = 5 (super)gravity on the background R4 × T1 at nonzero temperature is calculated with accuracy to linear curvature terms. Vacuum energy for open and closed superstrings with broken supersymmetry on the background M4 × T6, where M4 is Minkowski space, is also obtained. The question of the possibility of spontaneous compactification in models under consideration is analyzed.

TWO-LOOP APPROACH TO THE EFFECTIVE ACTION IN QUANTUM GRAVITY

1992 ◽  
Vol 07 (14) ◽  
pp. 3203-3233 ◽  
Author(s):  
I. L. BUCHBINDER ◽  
S. D. ODINTSOV ◽  
O. A. FONAREV
Keyword(s):  
Quantum Gravity ◽  
Cosmological Constant ◽  
Minkowski Space ◽  
Effective Action ◽  
Dimensional Regularization ◽  
Dimensional Torus ◽  
Spontaneous Compactification ◽  
Metric Tensor ◽  
First Time

For the first time we present the general formalism and results of calculation of the two-loop effective action in Einstein quantum gravity on the background MN × Tk, where MN is Minkowski space and Tk is a k-dimensional torus. We discuss the case of a zero cosmological constant as well as of a nonzero one. The method of calculating variations of the action on a metric tensor and the technique of calculating momentum integrals in dimensional regularization are presented. Some applications to spontaneous compactification are discussed, as well as some prospects.

scholarly journals On the component structure of one-loop effective actions in 6D, 𝒩 = (1,0) and 𝒩 = (1,1) supersymmetric gauge theories

2019 ◽  
Vol 35 (09) ◽  
pp. 2050060 ◽  
Author(s):  
I. L. Buchbinder ◽  
A. S. Budekhina ◽  
B. S. Merzlikin
Keyword(s):  
Effective Potential ◽  
Effective Action ◽  
Gauge Theories ◽  
Scalar Fields ◽  
Low Energy ◽  
Supersymmetric Gauge Theories ◽  
Component Structure ◽  
Yang Mills ◽  
Supersymmetric Gauge ◽  
The One

We study the six-dimensional [Formula: see text] and [Formula: see text] supersymmetric Yang–Mills (SYM) theories in the component formulation. The one-loop divergencies of effective action are calculated. The leading one-loop low-energy contributions to bosonic sector of effective action are found. It is explicitly demonstrated that the contributions to effective potential for the constant background scalar fields are absent in the [Formula: see text] SYM theory.

CASIMIR EFFECT IN MULTIDIMENSIONAL QUANTUM SUPER-GRAVITIES AND SUPERSYMMETRY BREAKING

1988 ◽  
Vol 03 (14) ◽  
pp. 1391-1399 ◽  
Author(s):  
S.D. ODINTSOV
Keyword(s):  
Effective Action ◽  
Casimir Effect ◽  
Gravitational Energy ◽  
Temperature Phase ◽  
Zero Temperature ◽  
Dimensional Torus ◽  
Curved Space ◽  
Temperature Phase Transition ◽  
The One ◽  
Kaluza Klein

The one-loop effective action (the Casimir gravitational energy) of the aribitrary Einstein supergravity on the background [Formula: see text], where [Formula: see text] is the Minkowski space with non-zero temperature, Td is the d-dimensional torus, is calculated. The problem of quantum breaking of supersymmetry is discussed. The Vilkovisky-De Witt effective action in the D-dimensional Einstein gravity with the Λ-term on the background [Formula: see text] is found. An idea is expressed that a temperature phase transition in Kaluza-Klein theories is possible. For d=5 gravity, the Vilkovisky-De Witt effective action on the [Formula: see text], where [Formula: see text] is four-dimensional curved space-time with non-zero temperature, is found.

scholarly journals TWO-FORM GRAVITY AND THE GENERATION OF SPACE-TIME

1996 ◽  
Vol 11 (17) ◽  
pp. 3033-3048
Author(s):  
MIYUKI KATSUKI ◽  
AKIO SUGAMOTO ◽  
SHIN’ICHI NOJIRI
Keyword(s):  
Effective Potential ◽  
Planck Scale ◽  
Conformal Factor ◽  
Einstein Gravity ◽  
Space Time ◽  
Gauge Condition ◽  
Cosmological Term ◽  
Divergent Term ◽  
Temporal Gauge ◽  
The One

In the framework of the two-form gravity, which is classically equivalent to the Einstein gravity, the one-loop effective potential for the conformal factor of metric is calculated in the finite volume and in the finite temperature by choosing a temporal gauge condition. There appears a quartically divergent term which cannot be removed by the renormalization of the cosmological term and we find there is only one nontrivial minimum in the effective potential. If the cutoff scale has a physical meaning, e.g. the Planck scale coming from string theory, this minimum might explain why the space-time is generated, i.e. why the classical metric has a nontrivial value.

Effective action of in Krein space quantization

2017 ◽  
Vol 95 (12) ◽  
pp. 1239-1241 ◽  
Author(s):  
B. Forghan ◽  
S. Razavi
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Effective Action ◽  
Regularization Method ◽  
Krein Space ◽  
Quantum Field ◽  
Kreĭn Space ◽  
Finite Solution ◽  
The One ◽  
Krein Space Quantization

The appearance of divergence creates computational issues in the process of calculating the one-loop effective action of [Formula: see text] in quantum field theory. In this paper, it is demonstrated that using Krein space quantization with Ford’s method of fluctuated metrics, divergence can be removed and that without using any traditional regularization method, it is possible to arrive at a finite solution for the effective action.

scholarly journals The renormalization group and the effective action

2011 ◽  
Vol 89 (3) ◽  
pp. 277-280 ◽  
Author(s):  
D. G.C. McKeon
Keyword(s):  
Renormalization Group ◽  
Scalar Field ◽  
Gauge Field ◽  
Effective Potential ◽  
Effective Action ◽  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
The One ◽  
External Gauge

The renormalization group is used to sum the leading-log (LL) contributions to the effective action for a large constant external gauge field in terms of the one-loop renormalization group (RG) function β, the next-to-leading-log (NLL) contributions in terms of the two-loop RG function, etc. The log-independent pieces are not determined by the RG equation, but can be fixed by considering the anomaly in the trace of the energy-momentum tensor. Similar considerations can be applied to the effective potential V for a scalar field [Formula: see text]; here the log-independent pieces are fixed by the condition [Formula: see text].

scholarly journals COMMENTS ABOUT THE GEOMETRY OF NONLINEAR SIGMA MODELS

1987 ◽  
Vol 02 (06) ◽  
pp. 1763-1772 ◽  
Author(s):  
ROBERT COQUEREAUX
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Sigma Models ◽  
Effective Action ◽  
Quantum Field ◽  
Geometrical Meaning ◽  
Perturbative Quantum ◽  
Perturbative Quantum Field Theory ◽  
The One ◽  
Nonlinear Sigma Models

Geometrical aspects of several classes of σ models are studied. The geometrical meaning of perturbative quantum field theory is discussed in the content of nonlinear σ models. Results on the one-loop effective action are recovered and generalized.

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