scholarly journals A note on gauge invariant operators in noncommutative gauge theories and the Matrix model

2000 ◽  
Vol 495 (3-4) ◽  
pp. 413-417 ◽  
Author(s):  
Avinash Dhar ◽  
Spenta R. Wadia
Keyword(s):  
Matrix Model ◽  
Gauge Theories ◽  
Gauge Invariant ◽  
The Matrix ◽  
Noncommutative Gauge Theories

scholarly journals ANOMALIES IN NONCOMMUTATIVE GAUGE THEORIES, SEIBERG–WITTEN TRANSFORMATION AND RAMOND–RAMOND COUPLINGS

2004 ◽  
Vol 19 (04) ◽  
pp. 613-630 ◽  
Author(s):  
RABIN BANERJEE
Keyword(s):  
Gauge Theory ◽  
Gauge Theories ◽  
Chern Character ◽  
Exact Expression ◽  
Gauge Invariant ◽  
Axial Anomaly ◽  
Noncommutative Gauge Theory ◽  
Noncommutative Gauge Theories

We propose an exact expression for the unintegrated form of the star gauge-invariant axial anomaly in an arbitrary even dimensional noncommutative gauge theory. The proposal is based on our earlier work,7 as well as on the inverse Seiberg–Witten map and identities related to it, obtained previously15,18 by comparing Ramond–Ramond couplings in different descriptions. The integrated anomalies, found from the unintegrated ones, are expressed in terms of a simplified version of the Elliott formula involving the noncommutative Chern character. These anomalies, under the Seiberg–Witten transformation, reduce to the ordinary (integrated) axial anomalies. Compatibility with existing results of anomalies in noncommutative theories is established.

MATRIX MODELS AND GAUGE-INVARIANT FIELD THEORY OF SUBCRITICAL STRINGS

1992 ◽  
Vol 07 (11) ◽  
pp. 2559-2588 ◽  
Author(s):  
ASHOKE SEN
Keyword(s):  
Field Theory ◽  
Partition Function ◽  
Matrix Models ◽  
Matrix Model ◽  
String Field Theory ◽  
Correlation Functions ◽  
Ward Identities ◽  
Gauge Invariant ◽  
The Matrix

A gauge-invariant interacting field theory of subcritical closed strings is constructed. It is shown that for d ≤ 1 this field theory reproduces many of the features of the corresponding matrix model. Among them are the scaling dimensions of the relevant primary fields, identities involving the correlation functions of some of the redundant operators in the matrix model, and the flow between different matrix models under appropriate perturbation. In particular, it is shown that some of the constraints on the partition function derived recently by Dijkgraaf et al. and Fukuma et al. may be interpreted as Ward identities in string field theory.

scholarly journals Strong-coupling results for $$ \mathcal{N} $$ = 2 superconformal quivers and holography

2021 ◽  
Vol 2021 (10) ◽  
Author(s):  
M. Billò ◽  
M. Frau ◽  
F. Galvagno ◽  
A. Lerda ◽  
A. Pini
Keyword(s):  
Strong Coupling ◽  
Matrix Model ◽  
Numerical Evaluation ◽  
Gauge Theories ◽  
Four Dimensions ◽  
Hooft Coupling ◽  
Planar Limit ◽  
The Matrix ◽  
Single Trace ◽  
Holographic Description

Abstract We consider $$ \mathcal{N} $$ N = 2 superconformal quiver gauge theories in four dimensions and evaluate the chiral/anti-chiral correlators of single-trace operators. We show that it is convenient to form particular twisted and untwisted combinations of these operators suggested by the dual holographic description of the theory. The various twisted sectors are orthogonal and the correlators in each sector have always the same structure, as we show at the lowest orders in perturbation theory with Feynman diagrams. Using localization we then map the computation to a matrix model. In this way we are able to obtain formal expressions for the twisted correlators in the planar limit that are valid for all values of the ‘t Hooft coupling λ, and find that they are proportional to 1/λ at strong coupling. We successfully test the correctness of our extrapolation against a direct numerical evaluation of the matrix model and argue that the 1/λ behavior qualitatively agrees with the holographic description.

scholarly journals PLANAR AND NONPLANAR KONISHI ANOMALIES AND EFFECTIVE SUPERPOTENTIAL FOR NONCOMMUTATIVE ${\mathcal N}=1$ SUPERSYMMETRIC U(1)

2005 ◽  
Vol 20 (13) ◽  
pp. 2859-2892 ◽  
Author(s):  
FARHAD ARDALAN ◽  
NÉDA SADOOGHI
Keyword(s):  
Gauge Theory ◽  
Gauge Field ◽  
Gauge Theories ◽  
Gauge Invariant ◽  
Noncommutative Gauge Theories

The Konishi anomalies for noncommutative [Formula: see text] supersymmetric U (1) gauge theory arising from planar and nonplanar diagrams are calculated. Whereas planar Konishi anomaly is the expected ⋆-deformation of the commutative anomaly, nonplanar anomaly reflects the important features of nonplanar diagrams of noncommutative gauge theories, such as UV/IR mixing and the appearance of nonlocal open Wilson lines. We use the planar and nonplanar Konishi anomalies to calculate the effective superpotential of the theory. In the limit of vanishing |Θp|, with Θ the noncommutativity parameter, the noncommutative effective superpotential depends on a gauge invariant superfield, which includes supersymmetric Wilson lines, and has nontrivial dependence on the gauge field supermultiplet.

Developing the basis of the matrix model of the regional innovation subsystem

2020 ◽  
Vol 18 (11) ◽  
pp. 2183-2204
Author(s):  
E.I. Moskvitina
Keyword(s):  
Russian Federation ◽  
Matrix Model ◽  
Federal District ◽  
Assessment Method ◽  
Expert Assessment ◽  
Regional Innovation ◽  
Regional Strategies ◽  
Analysis And Synthesis ◽  
The Matrix ◽  
The Russian Federation

Subject. This article deals with the issues related to the formation and implementation of the innovation capacity of the Russian Federation subjects. Objectives. The article aims to develop the organizational and methodological foundations for the formation of a model of the regional innovation subsystem. Methods. For the study, I used the methods of analysis and synthesis, economics and statistics analysis, and the expert assessment method. Results. The article presents a developed basis of the regional innovation subsystem matrix model. It helps determine the relationship between the subjects and the parameters of the regional innovation subsystem. To evaluate the indicators characterizing the selected parameters, the Volga Federal District regions are considered as a case study. The article defines the process of reconciliation of interests between the subjects of regional innovation. Conclusions. The results obtained can be used by regional executive bodies when developing regional strategies for the socio-economic advancement of the Russian Federation subjects.

scholarly journals Exact 1/N expansion of Wilson loop correlators in $$ \mathcal{N} $$ = 4 Super-Yang-Mills theory

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Wolfgang Mück
Keyword(s):  
Matrix Model ◽  
Wilson Loop ◽  
Model Solution ◽  
Wilson Loops ◽  
Combinatorial Formula ◽  
Expectation Value ◽  
Yang Mills ◽  
Hooft Coupling ◽  
The Matrix ◽  
Super Yang Mills Theory

Abstract Supersymmetric circular Wilson loops in $$ \mathcal{N} $$ N = 4 Super-Yang-Mills theory are discussed starting from their Gaussian matrix model representations. Previous results on the generating functions of Wilson loops are reviewed and extended to the more general case of two different loop contours, which is needed to discuss coincident loops with opposite orientations. A combinatorial formula representing the connected correlators of multiply wound Wilson loops in terms of the matrix model solution is derived. Two new results are obtained on the expectation value of the circular Wilson loop, the expansion of which into a series in 1/N and to all orders in the ’t Hooft coupling λ was derived by Drukker and Gross about twenty years ago. The connected correlators of two multiply wound Wilson loops with arbitrary winding numbers are calculated as a series in 1/N. The coefficient functions are derived not only as power series in λ, but also to all orders in λ by expressing them in terms of the coefficients of the Drukker and Gross series. This provides an efficient way to calculate the 1/N series, which can probably be generalized to higher-point correlators.

scholarly journals Divergent ⇒ complex amplitudes in two dimensional string theory

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Ashoke Sen
Keyword(s):  
Scattering Amplitudes ◽  
String Theory ◽  
Matrix Model ◽  
Two Dimensional ◽  
Full Matrix ◽  
Instanton Contribution ◽  
The Matrix ◽  
Theory Result ◽  
The One ◽  
Remarkable Agreement

Abstract In a recent paper, Balthazar, Rodriguez and Yin found remarkable agreement between the one instanton contribution to the scattering amplitudes of two dimensional string theory and those in the matrix model to the first subleading order. The comparison was carried out numerically by analytically continuing the external energies to imaginary values, since for real energies the string theory result diverges. We use insights from string field theory to give finite expressions for the string theory amplitudes for real energies. We also show analytically that the imaginary parts of the string theory amplitudes computed this way reproduce the full matrix model results for general scattering amplitudes involving multiple closed strings.

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