Topological Strings and Integrable Hierarchies
By Mina Aganagic, R. Dijkgraaf, A. Klemm, Marcos Mariño, C. Vafa. 2003
551 citations recorded by the source corpus.
We consider the topological B-model on local Calabi-Yau geometries. We show how one can solve for the amplitudes by using -algebra symmetries which encode the symmetries of holomorphic diffeomorphisms of the Calabi-Yau. In the highly effective fermionic/brane formulation this leads to a free fermion description of the amplitudes. Furthermore we argue that topological strings on Calabi-Yau geometries provide a unifying picture connecting non-critical (super)strings, integrable hierarchies, and various matrix models. In particular we show how the ordinary matrix model, the double scaling limit of matrix models, and Kontsevich-like matrix model are all related and arise from studying branes in specific local Calabi-Yau three-folds. We also show how an A-model topological string on P1 and local toric threefolds (and in particular the topological vertex) can be realized and solved as B-model topological string amplitudes on a Calabi-Yau manifold.
Subfields: Geometry and Topology, Nuclear and High Energy Physics
View Paper: https://www.semanticscholar.org/paper/63a1949426a2315d1edd4dbbc3d360a79798b044
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Citations in the corpus
- Vortex Counting and Lagrangian 3-Manifolds (2010, background): “This is expected from the description of a surface operator as a Lagrangian brane in the open BPS theory, since such a Lagrangian brane is well-known to have a dual description as a free fermion field [54, 55, 56].”
- Topological Strings from Quantum Mechanics (2014, background): “Aspects of this correspondence have been explored in various papers, starting in [15] and, more relevant to our purposes, in [16, 17], building on the work of [13] for gauge theories.”
- Symmetries of Tree-level Scattering Amplitudes in N = 6 Superconformal Chern{Simons Theory (2010, background): “1) for a given symmetric form gij, where i;j= 1;:::2k, then the objects Tij ˘ i; j ; (A.2) satisfy the so(2k) algebra commutation relations Tij;Tkl ˘gjkTil+ ::: (A.3) 16See also [42] for osp(Nj4) and [43] for sp(2‘). 32 where the dots mean: Add three more terms such that the symmetry properties of t”
- Liouville Correlation Functions from Four-Dimensional Gauge Theories (2009, background): “rmal block. Find a physical explanation of this transformation law. cf. [22]. 4. What is the relation of the Liouville theory and the theory of chiral bosons ubiquitous in the topological vertex? cf. [23, 24]. 5. We found that Liouville correlators are the integral of the absolute value squared of N”
- Remodeling the B-Model (2007, methodology): “In [40] it was argued that this more general construction attached to an arbitrary Riemann surface computes the amplitudes of the chiral boson theory described in [2], and in particular that the formalism of [23] should give the solution to the B-model for mirrors of toric geometries, providing in t”
- Liouville Field Theory — A decade after the revolution (2004, methodology): “In [122], the equivalence of the description from the double scaling matrix model and the Kontsevich matrix model is studied from the topological string perspective.”
- Quantum Riemann Surfaces in Chern-Simons Theory (2011, background): “It is argued in [23] that in fact Z(x) should be treated as a wavefunction that is annihilated by a quantized version of the Riemann surface Σ, i.”
- Knot Homology from Refined Chern-Simons Theory (2011, background): “In the topological string the operation of obtaining the partition function on Y from sewing partition functions on YL an YR is familiar, see for example [49,44,59].”
- Topological M-theory as unification of form theories of gravity (2004, methodology): “This theory can also be viewed [16,17] as the effective theory of the B model topological string on the Calabi-Yau 3-fold uv = F (x, p), where F (x, p) = 0 denotes the Fermi surface.”
- Two Dimensional Yang-Mills, Black Holes and Topological Strings (2004, background): “Ztop → Ztop(t + lmgs) where the coefficient m enters here because of the intersection of T 2 with C4 as was explained in [22].”
- Topological Strings and (Almost) Modular Forms (2006, methodology): “For example, the B-model on all non-compact toric Calabi-Yau manifolds was solved to all genera in [1] using the W∞ symmetries of the theory.”
- Topological String Theory on Compact Calabi–Yau: Modularity and Boundary Conditions (2006, background): “- [1] or large N-techniques [2] and has intriguing connections to Chern-Simons theory [3], open-closed string duality [4], matrix models [5], integrable hierarchies of non-critical string theory [6] and 2d Yang-Mills theory [7].”
- Hurwitz numbers, matrix models and enumerative geometry (2007, background): “hysical reason for the claim in [M] is that the theory of matrix models is just an example of a more general construction, namely a chiral boson on a “quantum” Riemann surface, as it was suggested in [ADKMV]. In this paper it was also argued that the B-model on the mirror of a toric Calabi–Yau three”
- Late Time Correlation Functions, Baby Universes, and ETH in JT Gravity (2019, methodology): “The rules for including D-brane boundaries do not have a clear origin in gravity; we must rely upon the matrix integral description of JT gravity to understand how to properly (31)These branes are also closely related to branes in topological string theories described by matrix models [64, 65, 66, 6”
- The refined topological vertex (2007, background): “(44) This relation was noted in [17] where it was related to the non-commutative geometry of the coordinates on the local mirror geometry.”