Unoriented strings, loop equations, and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="bold-script">N</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn><mml:mn /></mml:math>superpotentials from matrix models

Ashok, Sujay K.; Corrado, Richard; Römelsberger, Christian; Kennaway, Kristian D.; Halmagyi, Nick

doi:10.1103/physrevd.67.086004

Cited by 48 publications

(110 citation statements)

References 70 publications

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“…In practice the 4 All quantities W , F, F in this paper that do not carry an explicit superscript referring to the group are for SO(N ). 5 The same result has been recently obtained using other methods [37,38]. In Ref.…”

Section: Loop Equationsupporting

confidence: 73%

“…In section 2 we present the factorization solution for SW curves for orthogonal groups and use this information to construct the effective glueball superpotential by integrating-in S. Then we discuss in section 3 how this result should be reproduced from a random matrix model following the DV proposal. This implies in particular a non-trivial relation between the spherical and RP 2 contribution to the free energy, as was also noted in [37,38]. Finally, in section 4 we prove for arbitrary tree level potentials the required random matrix identity using loop equation techniques.…”

Section: Introductionmentioning

confidence: 91%

“…According to the conjecture of [3] (in the form given in Refs. [37,38] for SO/Sp), the perturbative part of the superpotential is then given by…”

Section: The Dijkgraaf-vafa Proposalmentioning

confidence: 99%

“…This is interesting as these involve nonorientable graphs on the random matrix side and especially as the original proposal of DV [3] was somewhat ambiguous (and indeed has to be slightly modified). Very recently, as this work was in progress, there appeared papers which addressed the orthogonal groups from different perspectives, namely perturbative methods [37] and CY/diagrammatic methods [38]. The interesting paper [38] has some overlap in that the loop equation is also used there.…”

Section: Introductionmentioning

confidence: 99%

“…Very recently, as this work was in progress, there appeared papers which addressed the orthogonal groups from different perspectives, namely perturbative methods [37] and CY/diagrammatic methods [38]. The interesting paper [38] has some overlap in that the loop equation is also used there. We differ, however, on various aspects of the derivation of the equation as well as the solution of it.…”

Section: Introductionmentioning

confidence: 99%

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SO(N) superpotential, Seiberg–Witten curves and loop equations

Janik¹,

Obers²

2003

Physics Letters B

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We consider the exact superpotential of N = 1 super Yang-Mills theory with gauge group SO(N ) and arbitrary tree-level polynomial superpotential of one adjoint Higgs field. A field-theoretic derivation of the glueball superpotential is given, based on factorization of the N = 2 Seiberg-Witten curve. Following the conjecture of Dijkgraaf and Vafa, the result is matched with the corresponding SO(N ) matrix model prediction. The verification involves an explicit solution of the first non-trivial loop equation, relating the spherical free energy to that of the non-orientable surfaces with topology RP 2 .

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Section: Loop Equationsupporting

confidence: 73%

Section: Introductionmentioning

confidence: 91%

“…According to the conjecture of [3] (in the form given in Refs. [37,38] for SO/Sp), the perturbative part of the superpotential is then given by…”

Section: The Dijkgraaf-vafa Proposalmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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SO(N) superpotential, Seiberg–Witten curves and loop equations

Janik¹,

Obers²

2003

Physics Letters B

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Subleading analysis for S3 partition functions of $$ \mathcal{N} $$ = 2 holographic SCFTs

Geukens,

Hong

2024

J. High Energ. Phys.

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We investigate the 3-sphere partition functions of various 3d $$ \mathcal{N} $$ N = 2 holographic SCFTs arising from the N stack of M2-branes in the ’t Hooft limit both analytically and numerically. We first employ a saddle point approximation to evaluate the free energy F = – log Z at the planar level, tracking the first subleading corrections in the large ’t Hooft coupling λ expansion. Subsequently, we improve these results by determining the planar free energy to all orders in the large λ expansion via numerical analysis. Remarkably, the resulting planar free energies turn out to take a universal form, supporting a prediction that these S3 partition functions are all given in terms of an Airy function even beyond the special cases where the Airy formulae were derived analytically in the literature; in this context we also present new Airy conjectures in several examples. The subleading behaviors we captured encode a part of quantum corrections to the M-theory path integrals around dual asymptotically Euclidean AdS4 backgrounds with the corresponding internal manifolds through holographic duality.

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Exact probes of orientifolds

Fiol

Garolera

Torrents

2014

J. High Energ. Phys.

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We compute the exact vacuum expectation value of circular Wilson loops for Euclidean N = 4 super Yang-Mills with G = SO(N ), Sp(N ), in the fundamental and spinor representations. These field theories are dual to type IIB string theory compactified on AdS 5 × RP 5 plus certain choices of discrete torsion, and we use our results to probe this holographic duality. We first revisit the LLM-type geometries having AdS 5 × RP 5 as ground state. Our results clarify and refine the identification of these LLM-type geometries as bubbling geometries arising from fermions on a half harmonic oscillator. We furthermore identify the presence of discrete torsion with the one-fermion Wigner distribution becoming negative at the origin of phase space. We then turn to the string world-sheet interpretation of our results and argue that for the quantities considered they imply two features: first, the contribution coming from world-sheets with a single crosscap is closely related to the contribution coming from orientable world-sheets, and second, world-sheets with two crosscaps don't contribute to these quantities.

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Unoriented strings, loop equations, andN=1superpotentials from matrix models

Cited by 48 publications

References 70 publications

SO(N) superpotential, Seiberg–Witten curves and loop equations

SO(N) superpotential, Seiberg–Witten curves and loop equations

Subleading analysis for S3 partition functions of $$ \mathcal{N} $$ = 2 holographic SCFTs

Exact probes of orientifolds

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