Holomorphic anomaly in gauge theories and matrix models

By Min-xin Huang, A. Klemm. 2006

147 citations recorded by the source corpus.

We use the holomorphic anomaly equation to solve the gravitational corrections to Seiberg-Witten theory and a two-cut matrix model, which is related by the Dijkgraaf-Vafa conjecture to the topological B-model on a local Calabi-Yau manifold. In both cases we construct propagators that give a recursive solution in the genus modulo a holomorphic ambiguity. In the case of Seiberg-Witten theory the gravitational corrections can be calculated to all genus as quasimodular functions of Γ(2). In the matrix model we fix the holomorphic ambiguity up to genus two. The latter result establishes the Dijkgraaf-Vafa conjecture at that genus and yields a new method for solving the matrix model at fixed genus in closed form in terms of generalized hypergeometric functions.

Subfields: Mathematical Physics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/8847f52bb32d738f904dd0f8b0eff2516ff26e09

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Citations in the corpus

Topological String Theory on Compact Calabi–Yau: Modularity and Boundary Conditions (2006, methodology): “In the local cases, which have elliptic curves as mirror geometry, we found [12, 13], that the above conditions (over)determine the unknowns in equations is provided by Hurwitz theory on elliptic curves [18].”
Refined stable pair invariants for E-, M- and [p, q]-strings (2013, methodology): “One can fix the holomorphic ambiguity using the gap boundary conditions proposed in [76, 78].”
Topological Strings and (Almost) Modular Forms (2006, background): “It is easy to show that [21] u(τ) = c+ d b (τ), (5.”
Remodeling the B-Model (2007, background): “Recently, boundary conditions have been found in the closed sector [32] (the so-called conifold gap condition and regularity at orbifold point) which fully fix these data in many local geometries (like the Seiberg–Witten geometry or local P(2)) [32, 28].”
Numerical studies of the ABJM theory for arbitrary N at arbitrary coupling constant (2012, background): “up to the constant map have been obtained for genus one and two in terms of modular forms as [29, 31, 48, 56] F (1) modular(λ) = − log η(τ) , (5.”
From Weak to Strong Coupling in ABJM Theory (2010, methodology): “Notice that the modular ring appearing here and parametrizing the holomorphic ambiguity is different from the one appearing in Seiberg–Witten theory [28,29] or in the cubic matrix model [58].”
Direct integration of the topological string (2007, methodology): “For genus up to 7 the expressions for F (g) were calculated in [33] using the Feynman graph expansion.”
Open string amplitudes and large order behavior in topological string theory (2006, methodology): “Following the philosophy of [23, 40, 1], one can obtain a modular invariant object by adding an antiholomorphic piece in the closed string moduli,”
The Ω Deformed B-model for Rigid N = 2 Theories (2011, methodology): “This coincides with the Picard-Fuchs equation used in [53].”