On the beta function in supersymmetric gauge theories

Carlino, Giuseppe; Konishi, Kenichi; Maggiore, Nicola; Magnoli, Nicodemo

doi:10.1016/s0370-2693(99)00454-2

Cited by 10 publications

(16 citation statements)

References 22 publications

(37 reference statements)

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“…The relation with normalization of the gauge coupling and the exact expression of the beta function was found in [27]. A simple exposition is given for example in [28]. is generated, where the determinant is taken to SU (2) and U Sp(N 2 ) as one flavor index.…”

Section: Deformed Conifold As Quantum Moduli Spacementioning

confidence: 99%

Remarks on orientifold projection in the conifold andSO×USpduality cascade

Imai

Yokono

2002

Phys. Rev. D

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We study the O3-plane in the conifold. On the D3-brane world-volume we obtain SO × U Sp gauge theory that exhibits a duality cascade phenomenon. The orientifold projection is determined on the type IIB string side, and corresponds to that of O4-plane on the dual type IIA side. We show that SUGRA solutions of Klebanov-Tseytlin and Klebanov-Strassler survive under the projection. We also investigate the orientifold projection in the generalized conifolds, and verify desired features of the O4-projection in the type IIA picture.

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Section: Deformed Conifold As Quantum Moduli Spacementioning

confidence: 99%

Remarks on orientifold projection in the conifold andSO×USpduality cascade

Imai

Yokono

2002

Phys. Rev. D

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“…This interpretation is however not valid for finite a for two reasons: firstly the statement that a is proportional to the gauge boson mass is only valid at weak coupling and secondly because (3.6) diverges at strong coupling, g → ∞ where τ → 0, [42,43]. The latter difficulty can be remedied by defining a different scaling function which is still a modular form of weight −2.…”

Section: Duality In Electromagnetismmentioning

confidence: 99%

“…The latter difficulty can be remedied by defining a different scaling function which is still a modular form of weight −2. Seiberg and Witten's expression for τ (u) can be inverted to give u(τ ) [40,41,42,43] …”

Section: Duality In Electromagnetismmentioning

confidence: 99%

Modular Symmetry and Fractional Charges in N = 2 Supersymmetric Yang-Mills and the Quantum Hall Effect

Dolan¹

2007

SIGMA

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Abstract. The parallel rôles of modular symmetry in N = 2 supersymmetric Yang-Mills and in the quantum Hall effect are reviewed. In supersymmetric Yang-Mills theories modular symmetry emerges as a version of Dirac's electric -magnetic duality. It has significant consequences for the vacuum structure of these theories, leading to a fractal vacuum which has an infinite hierarchy of related phases. In the case of N = 2 supersymmetric Yang-Mills in 3 + 1 dimensions, scaling functions can be defined which are modular forms of a subgroup of the full modular group and which interpolate between vacua. Infra-red fixed points at strong coupling correspond to θ-vacua with θ a rational number that, in the case of pure SUSY Yang-Mills, has odd denominator. There is a mass gap for electrically charged particles which can carry fractional electric charge. A similar structure applies to the 2 + 1 dimensional quantum Hall effect where the hierarchy of Hall plateaux can be understood in terms of an action of the modular group and the stability of Hall plateaux is due to the fact that odd denominator Hall conductivities are attractive infra-red fixed points. There is a mass gap for electrically charged excitations which, in the case of the fractional quantum Hall effect, carry fractional electric charge.

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“…The massless spectrum of type IIB superstring theory was given in the last section, where we found that in terms of transverse SO (8) 14 The relation between open-and closed-string couplings comes from the vertex operators for open-and closedstrings. The first one acts on the boundary, and the second on the interior of the worldsheet.…”

Section: Type Iib Supergravitymentioning

confidence: 81%

“…The bare lagrangian of an N = 1 supersymmetric gauge theory with generic matter content is given by [13][14][15],…”

Section: The Non-abelian Casementioning

confidence: 99%

Topics in gauge/gravity dualities

Romero¹

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Specially to Dr. Faraggi, who spent a lot of his pos-doctoral research time in IFUSP to try to teach me the necessary to face true theoretical physics, concepts, calculations and attitude.To Dr. Dmitry Melnikov from IIP-UFRN, for his patience to answer some questions by email, give ideas and recommend excellent references.To Dr. Jorge Noronha from IFUSP, for his comments during my thesis defense and also his detailed corrections.To IFUSP and CNPq for the financial support that allowed to make confortable my life and studies out of my country.Agradezco a mis padres, Juan y María, que me han ayudado y acompañado hasta ahora.Sin su apoyo no hubiese podido llegar hasta aquí. A mis amigos, Jonathan, Pedro y Pepe, que afortunadamente no son físicos, por su compañia a la distancia. Y a Laura.ii iii "There is geometry in the humming of the strings.There is music in the spacing of the spheres." Pythagoras ResumoEssa tese consiste num estudo autocontido das dualidades calibre/gravidade na linha do modelo do Klebanov-Witten. Aqui nos exploramos primeiro de um jeito razoavelmente detalhado,a conhecida dualidade do Maldacena que relaciona a teoria N = 4 SYM em quatro dimensões com as supercordas tipo IIB no espaço AdS 5 × S 5 , depois de alguns preliminares necessários sobre teorias supersimétricas de calibre, onde nós mostramos em detalhe aálgebra supersimétrica e as representações para N ≥ 1 supersimetria. Nós também construímos os conhecidos supercampos que sãoúteis para escrever lagrangianas invariantes para teorias de calibre facilmente, e então serãoúteis para construir a teoría de calibre do modelo de Klebanov-Witten. Na correspondência AdS/CFT original e as suas extensões fenomenologicamente interessantes, as Dp-branas, como soluções de supergravidade e objetos não perturbativos na teoria de cordas onde as teorias de calibre moram, são essenciais. Assim ,a fim de preservar a natureza autocontida desse trabalho, nós incluímos uma breve revisão sobre teoria de supercordas dirigida a entender a necessidade de incluir esses objetos extra-dimensionais usando dualidade-T e, no limite de baixa-energia da teoria de cordas, como soluções das equações de Einstein. O primeiro clímax desse trabalho ocorre quando nós usamos tudo o que aprendemos para estabelecer a conjectura do Maldacena, a teoria de calibre N = 4 SYM que nós estudamos no capítulo de supersimetria, morando no volume de mundo quadridimensional de uma pilha de N c D3-branas (sim, o subscrito "c" significa cor!) em espaço plano, corresponde exatamenteà teoria de supergravidade tipo IIB no espaço AdS 5 × S 5 .A fim de testar ela, nós identificamos simetrias e operadores com estados em ambos lados da dualidade. Mas na verdade isto correspondeà forma fraca da correspondência, porque nãoé possível lidar nem com a teoria de cordas nem com a teoria de calibre no limite de acoplamento forte.O foco e motivo principal de porque nós temos que aprender as primeiras cem páginas aqui, será estender a teoria de calibre dual que estudamos em AdS/CFT, para teorias de calibre mais r...

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On the beta function in supersymmetric gauge theories

Cited by 10 publications

References 22 publications

Remarks on orientifold projection in the conifold andSO×USpduality cascade

Remarks on orientifold projection in the conifold andSO×USpduality cascade

Modular Symmetry and Fractional Charges in N = 2 Supersymmetric Yang-Mills and the Quantum Hall Effect

Topics in gauge/gravity dualities

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