A Perturbative Window into Non-Perturbative Physics

By R. Dijkgraaf, C. Vafa. 2002

549 citations recorded by the source corpus.

We argue that for a large class of N=1 supersymmetric gauge theories the effective superpotential as a function of the glueball chiral superfield is exactly given by a summation of planar diagrams of the same gauge theory. This perturbative computation reduces to a matrix model whose action is the tree-level superpotential. For all models that can be embedded in string theory we give a proof of this result, and we sketch an argument how to derive this more generally directly in field theory. These results are obtained without assuming any conjectured dualities and can be used as a systematic method to compute instanton effects: the perturbative corrections up to n-th loop can be used to compute up to n-instanton corrections. These techniques allow us to see many non-perturbative effects, such as the Seiberg-Witten solutions of N=2 theories, the consequences of Montonen-Olive S-duality in N=1* and Seiberg-like dualities for N=1 theories from a completely perturbative planar point of view in the same gauge theory, without invoking a dual description.

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

View Paper: https://www.semanticscholar.org/paper/70d0d6c09d1637febffbbde84e19e74b75b3bf3c

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. N. Seiberg
3. E. Witten
4. C. Vafa
5. A. Klemm
6. Mina Aganagic
7. Y. Nakayama
8. F. Cachazo

In Nuclear and High Energy Physics

1. C. Vafa
2. Marcos Mariño
3. Mina Aganagic
4. A. Klemm
5. N. Seiberg
6. E. Witten
7. R. Dijkgraaf
8. Y. Nakayama

In Statistical and Nonlinear Physics

1. Marcos Mariño
2. C. Vafa
3. A. Klemm
4. Mina Aganagic
5. E. Witten
6. Y. Nakayama
7. R. Dijkgraaf
8. N. Seiberg

Citations in the corpus

• Chiral Rings and Anomalies in Supersymmetric Gauge Theory (2002, background): “In the early and mid-1990’s, holomorphy of the effective superpotential and gauge couplings were used, together with numerous other arguments, to obtain many nonperturbative results about supersymmetric dynamics.”
• Perturbative analysis of gauged matrix models (2002, unknown): “Following the notations of [3], henceforth we set g = 1.”
• BPS/CFT correspondence: non-perturbative Dyson-Schwinger equations and qq-characters (2015, background): “It appears that the exact computations of [24], [25] of effective superpotentials of N = 1 theories and their gravitational descendands can be cast in the form of the non-perturbative Dyson-Schwinger identities.”
• Axion inflation in type II string theory (2007, background): “We will briefly discuss their properties in various orientifold compactifications: D1 superpotentials in type I [33], D1 dependences through the determinants in the D3 instanton superpotentials [35, 36, 37], and gaugino condensates on space-time filling D5 branes [29, 30, 31, 32].”
• Matrix models, geometric engineering and elliptic genera (2003, methodology): “2 The matrix model approach In this section we discuss how we can obtain results for prepotential ofN = 2 supersymmetric theories in 4 dimensions, obtained from compactification of gauge theories in 6 dimensions on T(2) using matrix model techniques [16] adapted to higher dimensional gauge theories ”
• Perturbative computation of glueball superpotentials (2002, methodology): “In the next section we see a dramatic simplification for the U(N) case with adjoint representation (or fundamental representations) which verifies the matrix integral proposal of [1].”
• Supersymmetric Gauge Theories, Intersecting Branes and Free Fermions (2007, background): “This should be possible, especially in view of the fact that relations between N = 1 theories and topological strings are already well-understood [4].”
• Liouville Field Theory — A decade after the revolution (2004, methodology): “This may seem rather complicated and less efficient if we are only interested in the double scaling limit, but this method has a lot of applications including the recent Dijkgraaf-Vafa conjecture [90, 91, 92], [93, 94, 95].”
• Toda Theories, Matrix Models, Topological Strings, and N=2 Gauge Systems (2009, methodology): “It would be intersting to study this further, and in particular consider its application to more general local Calabi-Yau geometries.”
• Extended N=1 super Yang-Mills theories (2007, unknown): “February 1, 2008”
• Les Houches lectures on matrix models and topological strings (2004, background): “6 Extensions and applications The results derived above can be extended to more complicated Calabi-Yau backgrounds with branes [28, 29].”
• Dynamical SUSY breaking in meta-stable vacua (2006, background): “The supersymmetric vacua of this theory have been much studied (see e.g. [ 30-32 ]). We”
• Instanton counting, Macdonald function and the moduli space of D-branes (2005, background): “In topological theory the correspondence can be established more precisely as equalities among partition functions of topological string/gauge theory.”