scholarly journals The NSVZ relations for $$ \mathcal{N} $$ = 1 supersymmetric theories with multiple gauge couplings

2021 ◽  
Vol 2021 (10) ◽  
Author(s):  
D. S. Korneev ◽  
D. V. Plotnikov ◽  
K. V. Stepanyantz ◽  
N. A. Tereshina
Keyword(s):  
Gauge Coupling ◽  
Coupling Constants ◽  
Abelian Gauge ◽  
Covariant Derivatives ◽  
Higher Derivative ◽  
Anomalous Dimensions ◽  
New Form ◽  
Gauge Couplings ◽  
Supersymmetric Gauge ◽  
Supersymmetric Theories

Abstract We investigate the NSVZ relations for $$ \mathcal{N} $$ N = 1 supersymmetric gauge theories with multiple gauge couplings. As examples, we consider MSSM and the flipped SU(5) model, for which they easily reproduce the results for the two-loop β-functions. For $$ \mathcal{N} $$ N = 1 SQCD interacting with the Abelian gauge superfield we demonstrate that the NSVZ-like equation for the Adler D-function follows from the NSVZ relations. Also we derive all-loop equations describing how the NSVZ equations for theories with multiple gauge couplings change under finite renormalizations. They allow describing a continuous set of NSVZ schemes in which the exact NSVZ β-functions are valid for all gauge coupling constants. Very likely, this class includes the HD+MSL scheme, which is obtained if a theory is regularized by Higher covariant Derivatives and divergences are removed by Minimal Subtractions of Logarithms. That is why we also discuss how one can construct the higher derivative regularization for theories with multiple gauge couplings. Presumably, this regularization allows to derive the NSVZ equations for such theories in all loops. In this paper we make the first step of this derivation, namely, the NSVZ equations for theories with multiple gauge couplings are rewritten in a new form which relates the β-functions to the anomalous dimensions of the quantum gauge superfields, of the Faddeev-Popov ghosts, and of the matter superfields. The equivalence of this new form to the original NSVZ relations follows from the extension of the non-renormalization theorem for the triple gauge-ghost vertices, which is also derived in this paper.

scholarly journals GRAVITATIONAL CORRECTION TO SU(5) GAUGE COUPLING UNIFICATION

2010 ◽  
Vol 25 (04) ◽  
pp. 283-293 ◽  
Author(s):  
JITESH R. BHATT ◽  
SUDHANWA PATRA ◽  
UTPAL SARKAR
Keyword(s):  
Gauge Theories ◽  
Gauge Coupling ◽  
Phenomenological Approach ◽  
Coupling Constants ◽  
Abelian Gauge ◽  
Higher Dimensional

The gravitational corrections to the gauge coupling constants of Abelian and non-Abelian gauge theories have been shown to diverge quadratically. Since this result will have interesting consequences, this has been analyzed by several authors from different approaches. We propose to discuss this issue from a phenomenological approach. We analyze the SU(5) gauge coupling unification and argue that the gravitational corrections to gauge coupling constants may not vanish when higher dimensional non-renormalizable terms are included in the problem.

scholarly journals Supersymmetry, quantum corrections, and the higher derivative regularization

2018 ◽  
Vol 191 ◽  
pp. 06002
Author(s):  
Konstantin Stepanyantz
Keyword(s):  
Anomalous Dimension ◽  
Quantum Corrections ◽  
Explicit Calculation ◽  
Yukawa Couplings ◽  
Higher Derivative ◽  
Anomalous Dimensions ◽  
Higher Covariant Derivative ◽  
Derivative Method ◽  
Abelian Case ◽  
Supersymmetric Theories

We investigate the structure of quantum corrections in N = 1 supersymmetric theories using the higher covariant derivative method for regularization. In particular, we discuss the non-renormalization theorem for the triple gauge-ghost vertices and its connection with the exact NSVZ β-function. Namely, using the finiteness of the triple gauge-ghost vertices we rewrite the NSVZ equation in a form of a relation between the β-function and the anomalous dimensions of the quantum gauge superfield, of the Faddeev-Popov ghosts, and of the matter superfields. We argue that it is this form that follows from the perturbative calculations, and give a simple prescription how to construct the NSVZ scheme in the non-Abelian case. These statements are confirmed by an explicit calculation of the three-loop contributions to the β-function containing Yukawa couplings. Moreover, we calculate the two-loop anomalous dimension of the ghost superfields and demonstrate that for doing this calculation it is very important that the quantum gauge superfield is renormalized non-linearly.

scholarly journals The all-loop perturbative derivation of the NSVZ $$\beta $$-function and the NSVZ scheme in the non-Abelian case by summing singular contributions

2020 ◽  
Vol 80 (9) ◽  
Author(s):  
K. V. Stepanyantz
Keyword(s):  
Renormalization Group ◽  
Beta Function ◽  
Covariant Derivatives ◽  
Anomalous Dimensions ◽  
Higher Covariant Derivative ◽  
Higher Covariant Derivatives ◽  
Loop Approximation ◽  
Abelian Case ◽  
Group Functions ◽  
Supersymmetric Gauge

AbstractThe perturbative all-loop derivation of the NSVZ $$\beta $$ β -function for $${{\mathcal {N}}}=1$$ N = 1 supersymmetric gauge theories regularized by higher covariant derivatives is finalized by calculating the sum of singularities produced by quantum superfields. These singularities originate from integrals of double total derivatives and determine all contributions to the $$\beta $$ β -function starting from the two-loop approximation. Their sum is expressed in terms of the anomalous dimensions of the quantum gauge superfield, of the Faddeev–Popov ghosts, and of the matter superfields. This allows obtaining the NSVZ equation in the form of a relation between the $$\beta $$ β -function and these anomalous dimensions for the renormalization group functions defined in terms of the bare couplings. It holds for an arbitrary renormalization prescription supplementing the higher covariant derivative regularization. For the renormalization group functions defined in terms of the renormalized couplings we prove that in all loops one of the NSVZ schemes is given by the HD + MSL prescription.

scholarly journals PREDICTIONS FOR NON-ABELIAN FINE STRUCTURE CONSTANTS FROM MULTIPLE POINT CRITICALITY

1994 ◽  
Vol 09 (29) ◽  
pp. 5155-5200 ◽  
Author(s):  
D.L. BENNETT ◽  
H.B. NIELSEN
Keyword(s):  
Gauge Theory ◽  
Lattice Gauge Theory ◽  
Planck Scale ◽  
Gauge Coupling ◽  
Coupling Constants ◽  
Multiple Point ◽  
Abelian Gauge ◽  
Lattice Gauge ◽  
Structure Constants ◽  
Diagonal Subgroup

In developing a model for predicting the non-Abelian gauge coupling constants, we argue for the phenomenological validity of a “principle of multiple point criticality.” This is supplemented with the assumption of an “(grand) antiunified” gauge group SMG N gen ~ U(1) N gen × SU(2) N gen × SU(3) N gen which, at the Planck scale, breaks down to the diagonal subgroup. (Ngen is the number of generations, which is assumed to be three.) According to this principle of multiple point criticality, the Planck scale experimental couplings correspond to multiple point couplings of the bulk phase transition of a lattice gauge theory (with SMG N gen ). Predictions from this principle agree with running non-Abelian couplings (after an extrapolation to the Planck scale using the assumption of a “desert”) to an accuracy of 7%. As an explanation for the existence of the multiple point, a speculative model using a glassy lattice gauge theory is presented.

scholarly journals Three-loop contribution of the Faddeev–Popov ghosts to the $$\beta $$-function of $$\mathcal{N}=1$$ supersymmetric gauge theories and the NSVZ relation

2019 ◽  
Vol 79 (9) ◽  
Author(s):  
M. D. Kuzmichev ◽  
N. P. Meshcheriakov ◽  
S. V. Novgorodtsev ◽  
I. E. Shirokov ◽  
K. V. Stepanyantz
Keyword(s):  
Gauge Theories ◽  
Anomalous Dimension ◽  
Beta Function ◽  
Supersymmetric Gauge Theories ◽  
Loop Contribution ◽  
Covariant Derivatives ◽  
Anomalous Dimensions ◽  
Higher Covariant Derivatives ◽  
Supersymmetric Gauge ◽  
Multiloop Calculations

Abstract We find the three-loop contribution to the $$\beta $$β-function of $$\mathcal{N}=1$$N=1 supersymmetric gauge theories regularized by higher covariant derivatives produced by the supergraphs containing loops of the Faddeev–Popov ghosts. This is done using a recently proposed algorithm, which essentially simplifies such multiloop calculations. The result is presented in the form of an integral of double total derivatives in the momentum space. The considered contribution to the $$\beta $$β-function is compared with the two-loop anomalous dimension of the Faddeev–Popov ghosts. This allows verifying the validity of the NSVZ equation written as a relation between the $$\beta $$β-function and the anomalous dimensions of the quantum superfields. It is demonstrated that in the considered approximation the NSVZ equation is satisfied for the renormalization group functions defined in terms of the bare couplings. The necessity of the nonlinear renormalization for the quantum gauge superfield is also confirmed.

scholarly journals One-dimensional soliton system of gauged kink and Q-ball

2019 ◽  
Vol 79 (9) ◽  
Author(s):  
A. Yu. Loginov ◽  
V. V. Gauzshtein
Keyword(s):  
Electric Field ◽  
Gauge Coupling ◽  
Scalar Fields ◽  
Coupling Constants ◽  
Gauge Model ◽  
Complex Scalar ◽  
Abelian Gauge ◽  
Small Perturbations ◽  
One Dimensional ◽  
Dimensional Soliton

Abstract In the present paper, we consider a $$(1 + 1)$$(1+1)-dimensional gauge model consisting of two complex scalar fields interacting with each other through an Abelian gauge field. When the model’s gauge coupling constants are set to zero, the model possesses non-gauged Q-ball and kink solutions that do not interact with each other. It is shown here that for nonzero gauge coupling constants, the model has a soliton solution describing the system that consists of interacting Q-ball and kink components. These two components of the kink-Q-ball system have opposite electric charges, meaning that the total electric charge of the system vanishes. The properties of the kink-Q-ball system are studied both analytically and numerically. In particular, it was found that the system possesses a nonzero electric field and is unstable with respect to small perturbations in the fields.

scholarly journals Radially and azimuthally excited states of a soliton system of vortex and Q-ball

2020 ◽  
Vol 80 (12) ◽  
Author(s):  
A. Yu. Loginov ◽  
V. V. Gauzshtein
Keyword(s):  
Angular Momentum ◽  
Excited States ◽  
Gauge Coupling ◽  
Coupling Constants ◽  
Thick Wall ◽  
Thin Wall ◽  
Two Dimensional ◽  
Abelian Gauge ◽  
Dimensional Soliton ◽  
Quantized Magnetic Flux

AbstractIn the present paper, we continue to study the two-dimensional soliton system that is composed of vortex and Q-ball components interacting with each other through an Abelian gauge field. This vortex-Q-ball system is electrically neutral as a whole, nevertheless it possesses a nonzero electric field. Moreover, the vortex-Q-ball system has a quantized magnetic flux and a nonzero angular momentum, and combines properties of topological and nontopological solitons. We investigate radially and azimuthally excited states of the vortex-Q-ball system along with the unexcited vortex-Q-ball system at different values of gauge coupling constants. We also ascertain the behaviour of the vortex-Q-ball system in several extreme regimes, including thin-wall and thick-wall regimes.

scholarly journals One-loop polarization operator of the quantum gauge superfield for 𝒩 = 1 SYM regularized by higher derivatives

2017 ◽  
Vol 32 (36) ◽  
pp. 1750194 ◽  
Author(s):  
A. E. Kazantsev ◽  
M. B. Skoptsov ◽  
K. V. Stepanyantz
Keyword(s):  
Polarization Operator ◽  
Special Choice ◽  
Yang Mills ◽  
Feynman Gauge ◽  
Covariant Derivatives ◽  
Higher Derivative ◽  
Loop Approximation ◽  
Higher Derivatives ◽  
Supersymmetric Gauge ◽  
Brst Invariance

We consider the general [Formula: see text] supersymmetric gauge theory with matter, regularized by higher covariant derivatives without breaking the BRST invariance, in the massless limit. In the [Formula: see text]-gauge we obtain the (unrenormalized) expression for the two-point Green function of the quantum gauge superfield in the one-loop approximation as a sum of integrals over the loop momentum. The result is presented as a sum of three parts: the first one corresponds to the pure supersymmetric Yang–Mills theory in the Feynman gauge, the second one contains all gauge-dependent terms, and the third one is the contribution of diagrams with a matter loop. For the Feynman gauge and a special choice of the higher derivative regulator in the gauge fixing term, we analytically calculate these integrals in the limit [Formula: see text]. In particular, in addition to the leading logarithmically divergent terms, which are determined by integrals of double total derivatives, we also find the finite constants.

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