Gravitational corrections in supersymmetric gauge theory and matrix models

By A. Klemm, Marcos Mariño, S. Theisen. 2002

164 citations recorded by the source corpus.

Gravitational corrections in N = 1 and N = 2 supersymmetric gauge theories are obtained from topological string amplitudes. We show how they are recovered in matrix model computations. This provides a test of the proposal by Dijkgraaf and Vafa beyond the planar limit. Both, matrix model and topological string theory, are used to check a conjecture of Nekrasov concerning these gravitational couplings in Seiberg-Witten theory. Our analysis is performed for those gauge theories which are related to the cubic matrix model, i.e. pure SU(2) Seiberg-Witten theory and N = 2 U(N) SYM broken to N = 1 via a cubic superpotential. We outline the computation of the topological amplitudes for the local Calabi-Yau manifolds which are relevant for these two cases.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/3557122221b2996021d021d53055b5423a9cd99c

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Astronomy and Astrophysics

1. Marcos Mariño
2. A. Klemm
3. C. Vafa
4. Mina Aganagic
5. Min-xin Huang
6. R. Dijkgraaf
7. Amer Iqbal
8. H. Kanno

In Nuclear and High Energy Physics

1. Marcos Mariño
2. C. Vafa
3. A. Klemm
4. Mina Aganagic
5. Min-xin Huang
6. H. Kanno
7. V. Bouchard
8. R. Dijkgraaf

In Statistical and Nonlinear Physics

1. Marcos Mariño
2. C. Vafa
3. A. Klemm
4. Mina Aganagic
5. Min-xin Huang
6. V. Bouchard
7. R. Dijkgraaf
8. Amer Iqbal

Citations in the corpus

• Quantum geometry of refined topological strings (2011, unknown): “, [64]) ∆1 = z1z2 , ∆2 = √ δ2 − 2(z1 + z2) , ∆3 = (δ(2) − 3z1)(2) − 6z2δ(2) + 9z(2) 2 + 14z1z2 , where κI(β) are β-dependent coefficients.”
• Gravity Induced C-Deformation (2003, unknown): “This prediction has already been tested in a number of cases: for the gravitational correction for N = 4 Yang-Mills in the third paper in [1], and for certain N = 2 supersymmetric gauge systems in [10,11].”
• Holomorphic anomaly in gauge theories and matrix models (2006, methodology): “Also at one loop the conjecture holds(6) [8, 10].”
• From Weak to Strong Coupling in ABJM Theory (2010, unknown): “These expressions differ from the ones in [66] in a permutation of the roots, as explained in [67].”
• Supersymmetric Gauge Theories, Intersecting Branes and Free Fermions (2007, background): “Including all string loop corrections the free fermion theory is elegantly formulated in terms of holonomic D-modules that replace the classical holomorphic curve in the quantum case.”
• Nonperturbative effects and nonperturbative definitions in matrix models and topological strings (2008, background): “6.1 General picture 41 6.2 A toy model 42 6.3 Holographic description and nonperturbative effects 44”
• Topological Strings and (Almost) Modular Forms (2006, methodology): “can be rewritten, using the results we have obtained so far, as [26]”
• Instanton Counting and Chern-Simons Theory (2002, background): “For the N = 2 D=4 SU(2) theory this has been confirmed by comparing the results from the topologically twisted theory and matrix model calculations [19, 27].”
• Hermitian matrix model free energy: Feynman graph technique for all genera (2005, unknown): “We consider solutions to the loop equations admitting multi-matrix integral representations [6, 12, 13].”
• Topological strings and Nekrasov's formulas (2003, result): “We have computed P (k) g for F0 and found a precise agreement with the results reported in [ 28 , 21]”
• Les Houches lectures on matrix models and topological strings (2004, methodology): “One finds, up to fourth order in the coupling constant β, the following result [45]:”