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 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 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 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.

scholarly journals COMMENTS ON THE BACKGROUND FIELD METHOD IN HARMONIC SUPERSPACE: NON-HOLOMORPHIC CORRECTIONS IN N=4 SYM

1998 ◽  
Vol 13 (20) ◽  
pp. 1623-1635 ◽  
Author(s):  
IOSEPH L. BUCHBINDER ◽  
SERGEI M. KUZENKO
Keyword(s):  
Effective Action ◽  
Background Field ◽  
Field Method ◽  
Vector Multiplet ◽  
Harmonic Superspace ◽  
Background Field Method ◽  
Field Formalism ◽  
The One

We analyze the one-loop effective action of N=4 SYM theory in the framework of the bakground field formalism in N=2 harmonic superspace. For the case of onshell background N=2 vector multiplet we prove that the effective action is free of harmonic singularities. When the lowest N=1 superspace component of the N=2 vector multiplet is switched off, the effective action of N=4 SYM theory is shown to coincide with obtained by Grisaru et al. on the base of the N=1 background field method. We compute the leading non-holomorphic corrections to the N=4 SU (2) SYM effective action.

scholarly journals New bi-harmonic superspace formulation of 4D, $$ \mathcal{N} $$ = 4 SYM theory

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
I. L. Buchbinder ◽  
E. A. Ivanov ◽  
V. A. Ivanovskiy
Keyword(s):  
Effective Action ◽  
Harmonic Superspace ◽  
Four Dimensions ◽  
Yang Mills ◽  
Convenient Tool ◽  
Leading Term

Abstract We develop a novel bi-harmonic $$ \mathcal{N} $$ N = 4 superspace formulation of the $$ \mathcal{N} $$ N = 4 supersymmetric Yang-Mills theory (SYM) in four dimensions. In this approach, the $$ \mathcal{N} $$ N = 4 SYM superfield constraints are solved in terms of on-shell $$ \mathcal{N} $$ N = 2 harmonic superfields. Such an approach provides a convenient tool of constructing the manifestly $$ \mathcal{N} $$ N = 4 supersymmetric invariants and further rewriting them in $$ \mathcal{N} $$ N = 2 harmonic superspace. In particular, we present $$ \mathcal{N} $$ N = 4 superfield form of the leading term in the $$ \mathcal{N} $$ N = 4 SYM effective action which was known previously in $$ \mathcal{N} $$ N = 2 superspace formulation.

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.

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.

scholarly journals Nonperturbative one-loop effective action for QED with Yukawa couplings

2018 ◽  
Vol 33 (27) ◽  
pp. 1850157 ◽  
Author(s):  
Theodore N. Jacobson ◽  
Tonnis ter Veldhuis
Keyword(s):  
Effective Action ◽  
Proper Time ◽  
Background Field ◽  
Field Approximation ◽  
Chiral Anomaly ◽  
Dirac Fermion ◽  
Yukawa Couplings ◽  
Time Formalism ◽  
The One ◽  
The Relationship

We derive the one-loop effective action for scalar, pseudoscalar, and electromagnetic fields coupled to a Dirac fermion in an extension of QED with Yukawa couplings. Using the Schwinger proper-time formalism and zeta-function regularization, we calculate the full nonperturbative effective action to one loop in the constant background field approximation. Our result is nonperturbative in the external fields, and goes beyond existing results in the literature which treat only the first nontrivial order involving the pseudoscalar. The result has an even and odd part, which are related to the modulus and phase of the fermion functional determinant. The even contribution to the effective action involves the modulus of the effective Yukawa couplings and is invariant under global chiral transformations while the odd contribution is proportional to the angle between the scalar and pseudoscalar couplings. In different limits the effective action reduces either to the Euler–Heisenberg effective action or the Coleman–Weinberg potential. We also comment on the relationship between the odd part of the effective action and the chiral anomaly in QED.

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