scholarly journals ON LOW-ENERGY EFFECTIVE ACTION OF NONCOMMUTATIVE HYPERMULTIPLET MODEL

2001 ◽  
Vol 16 (40) ◽  
pp. 2591-2603 ◽  
Author(s):  
I. B. SAMSONOV
Keyword(s):  
Effective Action ◽  
Adjoint Representation ◽  
Low Energy ◽  
Coupling Constants ◽  
Quantum Corrections ◽  
Fundamental Representation ◽  
Harmonic Superspace ◽  
Commutative Case ◽  
The One ◽  
External Gauge

We consider the noncommutative hypermultiplet model within harmonic superspace approach. The one-loop four-point contributions to the effective action of self-interacting q-hypermultiplet are computed. This model has two coupling constants instead of a single one in commutative case. It is shown that both coupling constants are generated by one-loop quantum corrections in the model of q-hypermultiplet interacting with vector multiplet. The holomorphic effective action of q-hypermultiplet in external gauge superfield is calculated. For the fundamental representation there is no uv/ir-mixing and the holomorphic potential is a ⋆-product generalization of a standard commutative one. For the adjoint representation of U(N) gauge group the leading contributions to the holomorphic effective action are given by the terms respecting for the uv/ir-mixing which are related to U(1) phase of U(N) group.

scholarly journals HOLOMORPHIC EFFECTIVE ACTION OF N=2 SYM THEORY FROM HARMONIC SUPERSPACE WITH CENTRAL CHARGES

2000 ◽  
Vol 15 (30) ◽  
pp. 1859-1877 ◽  
Author(s):  
S. EREMIN ◽  
E. IVANOV
Keyword(s):  
Effective Action ◽  
Coupled System ◽  
Adjoint Representation ◽  
Coulomb Branch ◽  
Harmonic Superspace ◽  
The One ◽  
Diagram Techniques

We compute the one-loop holomorphic effective action of the massless Cartan sector of N=2 SYM theory in the Coulomb branch, taking into account the contributions both from the charged hypermultiplets and off-diagonal components of the gauge superfield. We use the manifestly supersymmetric harmonic superfields diagram techniques adapted to N=2 supersymmetry with the central charges induced by Cartan generators. The (anti)holomorphic part proves to be proportional to the central charges and it has the generic form of Seiberg's action obtained by integrating U (1)R anomaly. It vanishes for N=4 SYM theory, i.e. the coupled system of N=2 gauge superfield and hypermultiplet in the adjoint representation.

scholarly journals Supergraph calculation of one-loop divergences in higher-derivative 6D SYM theory

2020 ◽  
Vol 2020 (8) ◽  
Author(s):  
I. L. Buchbinder ◽  
E. A. Ivanov ◽  
B. S. Merzlikin ◽  
K. V. Stepanyantz
Keyword(s):  
Effective Action ◽  
A Priori ◽  
Coupling Constant ◽  
Harmonic Superspace ◽  
Classical Action ◽  
Higher Derivative ◽  
Component Approach ◽  
Dimensionless Coupling ◽  
The One ◽  
Dimensionless Coupling Constant

Abstract We apply the harmonic superspace approach for calculating the divergent part of the one-loop effective action of renormalizable 6D, $$ \mathcal{N} $$ N = (1, 0) supersymmetric higher-derivative gauge theory with a dimensionless coupling constant. Our consideration uses the background superfield method allowing to carry out the analysis of the effective action in a manifestly gauge covariant and $$ \mathcal{N} $$ N = (1, 0) supersymmetric way. We exploit the regularization by dimensional reduction, in which the divergences are absorbed into a renormalization of the coupling constant. Having the expression for the one-loop divergences, we calculate the relevant β-function. Its sign is specified by the overall sign of the classical action which in higher-derivative theories is not fixed a priori. The result agrees with the earlier calculations in the component approach. The superfield calculation is simpler and provides possibilities for various generalizations.

scholarly journals PROJECTIVE SUPERSPACE AS A DOUBLE-PUNCTURED HARMONIC SUPERSPACE

1999 ◽  
Vol 14 (11) ◽  
pp. 1737-1757 ◽  
Author(s):  
SERGEI M. KUZENKO
Keyword(s):  
Effective Action ◽  
Low Energy ◽  
Harmonic Superspace ◽  
Yang Mills ◽  
Projective Superspace ◽  
The Relationship

We analyze the relationship between the N=2 harmonic and projective superspaces, which are the only approaches developed to describe general N=2 super-Yang–Mills theories in terms of off-shell supermultiplets with conventional supersymmetry. The structure of low energy hypermultiplet effective action is briefly discussed.

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.

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].

TOPOLOGICAL CHANGES, CPT AND COMMUTATIVITY OF OPERATOR COUPLING CONSTANTS

1989 ◽  
Vol 04 (05) ◽  
pp. 409-417 ◽  
Author(s):  
P. G. TINYAKOV
Keyword(s):  
Effective Action ◽  
Low Energy ◽  
Coupling Constants ◽  
Planck Length ◽  
Cpt Symmetry ◽  
Different Types ◽  
Suitable Generalization ◽  
The Creation ◽  
Baby Universes ◽  
Topological Changes

We study the low energy effective action that takes into account the creation of baby universes at short (Planck) scales. We derive the restrictions imposed on the general form of the effective action by a suitable generalization of the CPT-symmetry. We find that if the operators creating baby universes of different types commute with each other, the operator coupling constants, present in the effective action, also commute with each other, i.e., they can be diagonalized simultaneously. This result implies that topological changes do not lead to nonlocality at scales large compared to the Planck length.

scholarly journals On a structure of the one-loop divergences in 4D harmonic superspace sigma-model

2022 ◽  
Vol 82 (1) ◽  
Author(s):  
I. L. Buchbinder ◽  
A. S. Budekhina ◽  
B. S. Merzlikin
Keyword(s):  
Effective Action ◽  
Sigma Model ◽  
Proper Time ◽  
Kähler Manifold ◽  
Quantum Structure ◽  
Harmonic Superspace ◽  
Component Structure ◽  
Covariant Derivatives ◽  
The One ◽  
Quantum Splitting

AbstractWe study the quantum structure of four-dimensional $${{\mathcal {N}}}=2$$ N = 2 superfield sigma-model formulated in harmonic superspace in terms of the omega-hypermultiplet superfield $$\omega $$ ω . The model is described by harmonic superfield sigma-model metric $$g_{ab}(\omega )$$ g ab ( ω ) and two potential-like superfields $$L^{++}_{a}(\omega )$$ L a + + ( ω ) and $$L^{(+4)}(\omega )$$ L ( + 4 ) ( ω ) . In bosonic component sector this model describes some hyper-Kähler manifold. The manifestly $${{\mathcal {N}}}=2$$ N = 2 supersymmetric covariant background-quantum splitting is constructed and the superfield proper-time technique is developed to calculate the one-loop effective action. The one-loop divergences of the superfield effective action are found for arbitrary $$g_{ab}(\omega ), L^{++}_{a}(\omega ), L^{(+4)}(\omega )$$ g ab ( ω ) , L a + + ( ω ) , L ( + 4 ) ( ω ) , where some specific analogy between the algebra of covariant derivatives in the sigma-model and the corresponding algebra in the $${{\mathcal {N}}}=2$$ N = 2 SYM theory is used. The component structure of divergences in the bosonic sector is discussed.

LOW ENERGY EFFECTIVE ACTION OF QUANTUM GRAVITY AND THE NATURALNESS PROBLEM

2013 ◽  
Vol 28 (03n04) ◽  
pp. 1340001 ◽  
Author(s):  
HIKARU KAWAI
Keyword(s):  
Wave Function ◽  
Quantum Gravity ◽  
Effective Action ◽  
Low Energy ◽  
Coupling Constants ◽  
Local Action ◽  
Topology Change ◽  
Dynamical Mechanism ◽  
Lorentzian Signature ◽  
The Universe

In quantum gravity or string theory, it is natural to take the topology change of the space into account. We consider the low energy effective action for such case and show that it does not have a simple form of the local action but has a multilocal form. Actually, in quantum gravity or matrix model, there are some mechanisms that the low energy effective action becomes S eff = ∑ici Si + ∑ijcijSiSj + ∑ijkcijk Si Sj Sk + ⋯, where Si is a local action of the form [Formula: see text]. We further discuss that the topology change of the space naturally leads to the multiverse in which indefinite number of macroscopic universes exist in parallel. In this case, the space–time coordinates x in the multilocal action may sit either in the same universe or in different ones. We then consider the wave function of the entire multiverse, and see how the locality and causality are recovered in such theory. We further discuss the possibility of solving the naturalness problem. In doing so, we need to introduce some assumptions to interpret the multiverse wave function. We consider two different possibilities. One is to simply assume the probabilistic interpretation for the multiverse wave function. The other is to assume infrared cutoff independence of the partition function of the universe. In both cases, we find that the big fix occurs, in which all the coupling constants in the low energy physics are determined by the dynamics of the multiverse. Actually, we find that they are fixed in such a way that the total entropy of the universe at the late stage (in the far future) is maximized. Although the argument here is similar to Coleman's original one given in the late 1980s, our results are based on Lorentzian signature theory and the dynamical mechanism is rather different.

scholarly journals On the alternative formulation of the three-dimensional noncommutative superspace

2016 ◽  
Vol 31 (10) ◽  
pp. 1650055 ◽  
Author(s):  
F. S. Gama ◽  
J. R. Nascimento ◽  
A. Yu. Petrov
Keyword(s):  
Effective Action ◽  
Three Dimensional ◽  
Low Energy ◽  
Alternative Formulation ◽  
Quantum Calculations ◽  
Point Function ◽  
The One ◽  
Chiral Superfield

In this paper, we propose a new version for the noncommutative superspace in 3D. This version is shown to be convenient for performing quantum calculations. In the paper, we use the theory of the chiral superfield as a prototype for possible generalizations, calculating the one-loop two-point function of a chiral superfield and the one-loop low-energy effective action in this theory.

scholarly journals Harmonic Superspace Approach to the Effective Action in Six-Dimensional Supersymmetric Gauge Theories

Symmetry ◽  
2019 ◽  
Vol 11 (1) ◽  
pp. 68 ◽  
Author(s):  
Ioseph Buchbinder ◽  
Evgeny Ivanov ◽  
Boris Merzlikin ◽  
Konstantin Stepanyantz
Keyword(s):  
Effective Action ◽  
Gauge Theories ◽  
Proper Time ◽  
Background Field ◽  
Field Method ◽  
Quantum Corrections ◽  
Supersymmetric Gauge Theories ◽  
Loop Approximation ◽  
Supersymmetric Gauge ◽  
The One

We review the recent progress in studying the quantum structure of 6 D , N = ( 1 , 0 ) , and N = ( 1 , 1 ) supersymmetric gauge theories formulated through unconstrained harmonic superfields. The harmonic superfield approach allows one to carry out the quantization and calculations of the quantum corrections in a manifestly N = ( 1 , 0 ) supersymmetric way. The quantum effective action is constructed with the help of the background field method that secures the manifest gauge invariance of the results. Although the theories under consideration are not renormalizable, the extended supersymmetry essentially improves the ultraviolet behavior of the lowest-order loops. The N = ( 1 , 1 ) supersymmetric Yang–Mills theory turns out to be finite in the one-loop approximation in the minimal gauge. Furthermore, some two-loop divergences are shown to be absent in this theory. Analysis of the divergences is performed both in terms of harmonic supergraphs and by the manifestly gauge covariant superfield proper-time method. The finite one-loop leading low-energy effective action is calculated and analyzed. Furthermore, in the Abelian case, we discuss the gauge dependence of the quantum corrections and present its precise form for the one-loop divergent part of the effective action.

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