M-theory and a topological string duality (original) (raw)
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M-Theory, Topological Strings and Spinning Black Holes
1999
We consider M-theory compactification on Calabi-Yau threefolds. The recently discovered connection between the BPS states of wrapped M2 branes and the topological string amplitudes on the threefold is used both as a tool to compute topological string amplitudes at higher genera as well as to unravel the degeneracies and quantum numbers of BPS states. Moduli spaces of kkk-fold symmetric products of the wrapped M2 brane play a crucial role. We also show that the topological string partition function is the Calabi-Yau version of the elliptic genus of the symmetric product of K3K3K3's and use the macroscopic entropy of spinning black holes in 5 dimensions to obtain new predictions for the asymptotic growth of the topological string amplitudes at high genera.
Topological twisting of multiple M2-brane theory
Journal of High Energy Physics, 2008
Bagger-Lambert-Gustavsson theory with infinite dimensional gauge group has been suggested to describe M5-brane as a condensation of multiple M2-branes. Here we perform a topological twisting of the Bagger-Lambert-Gustavsson theory. The original SO(8) R-symmetry is broken to SO(3)XSO(5), where the former may be interpreted as a diagonal subgroup of the Euclidean M5-brane world-volume symmetry SO(6), while the latter is the isometry of the transverse five directions. Accordingly the resulting action contains an one-form and five scalars as for the bosonic dynamical fields. We further lift the action to a generic curved three manifold. In order to make sure the genuine topological invariance, we construct an off-shell formalism such that the scalar supersymmetry transformations are nilpotent strictly off-shell and independent of the metric of the three manifold. The one loop partition function around a trivial background yields the Ray-Singer torsion. The BPS equation involves an M2-brane charge density given by a Nambu-Goto action defined in an internal three-manifold.
Mathematical structures of non-perturbative topological string theory: from GW to DT invariants
2021
We study the Borel summation of the Gromov–Witten potential for the resolved conifold. The Stokes phenomena associated to this Borel summation are shown to encode the Donaldson–Thomas invariants of the resolved conifold, having a direct relation to the Riemann–Hilbert problem formulated by T. Bridgeland. There exist distinguished integration contours for which the Borel summation reproduces previous proposals for the non-perturbative topological string partition functions of the resolved conifold. These partition functions are shown to have another asymptotic expansion at strong topological string coupling. We demonstrate that the Stokes phenomena of the strong-coupling expansion encode the DT invariants of the resolved conifold in a second way. Mathematically, one finds a relation to Riemann–Hilbert problems associated to DT invariants which is different from the one found at weak coupling. The Stokes phenomena of the strong-coupling expansion turn out to be closely related to the ...
Multiple self-dual strings on M5-branes
Journal of High Energy Physics, 2010
We show how to define Chern-Simons matter theories with boundary. Rather than imposing boundary conditions, we introduce new boundary degrees of freedom from the beginning and show how they can be used to cancel the gauge noninvariance of the Chern-Simons action. We apply this method to the ABJM theory with boundary. By imposing also boundary conformal invariance, we determine the required boundary action. This result allows us to derive the action for the multiple self-dual strings living on M5-branes.
Topological strings, two-dimensional Yang-Mills theory and Chern-Simons theory on torus bundles
Advances in Theoretical and Mathematical Physics, 2008
We study the relations between two-dimensional Yang-Mills theory on the torus, topological string theory on a Calabi-Yau threefold whose local geometry is the sum of two line bundles over the torus, and Chern-Simons theory on torus bundles. The chiral partition function of the Yang-Mills gauge theory in the large N limit is shown to coincide with the topological string amplitude computed by topological vertex techniques. We use Yang-Mills theory as an efficient tool for the computation of Gromov-Witten invariants and derive explicitly their relation with Hurwitz numbers of the torus. We calculate the Gopakumar-Vafa invariants, whose integrality gives a non-trivial confirmation of the conjectured nonperturbative relation between two-dimensional Yang-Mills theory and topological string theory. We also demonstrate how the gauge theory leads to a simple combinatorial solution for the Donaldson-Thomas theory of the Calabi-Yau background. We match the instanton representation of Yang-Mills theory on the torus with the nonabelian localization of Chern-Simons gauge theory on torus bundles over the circle. We also comment on how these results can be applied to the computation of exact degeneracies of BPS black holes in the local Calabi-Yau background.
Physics Letters B, 1995
It is shown that two dimensional (2d) topological gravity in the conformal gauge has a larger symmetry than has been hitherto recognized; in the formulation of Labastida, Pernici and Witten it contains a twisted "small" N = 4 superconformal symmetry. There are in fact two distinct twisted N = 2 structures within this N = 4, one of which is shown to be isomorphic to the algebra discussed by the Verlindes and the other corresponds, through bosonization, to c M ≤ 1 string theory discussed by Bershadsky et.al. As a byproduct, we find a twisted N = 4 structure in c M ≤ 1 string theory. We also study the "mirror" of this twisted N = 4 algebra and find that it corresponds, through another bosonization, to a constrained topological sigma model in complex dimension one.
Topological open/closed string dualities: matrix models and wave functions
Journal of High Energy Physics
We sharpen the duality between open and closed topological string partition functions for topological gravity coupled to matter. The closed string partition function is a generalized Kontsevich matrix model in the large dimension limit. We integrate out off-diagonal degrees of freedom associated to one source eigenvalue, and find an open/closed topological string partition function, thus proving open/closed duality. We match the resulting open partition function to the generating function of intersection numbers on moduli spaces of Riemann surfaces with boundaries and boundary insertions. Moreover, we connect our work to the literature on a wave function of the KP integrable hierarchy and clarify the role of the extended Virasoro generators that include all time variables as well as the coupling to the open string observable.
E-strings and N = 4 topological Yang-Mills theories
Nuclear Physics B, 1998
We study certain properties of six-dimensional tensionless E-strings (arising from zero size E 8 instantons). In particular we show that n E-strings form a bound string which carries an E 8 level n current algebra as well as a left-over conformal system with c = 12n − 4 − 248n n+30 , whose characters can be computed. Moreover we show that the characters of the n-string bound state are captured by N = 4 U (n) topological Yang-Mills theory on 1 2 K3. This relation not only illuminates certain aspects of E-strings but can also be used to shed light on the properties of N = 4 topological Yang-Mills theories on manifolds with b + 2 = 1. In particular the E-string partition functions, which can be computed using local mirror symmetry on a Calabi-Yau threefold , give the Euler characteristics of the Yang-Mills instanton moduli space on 1 2 K3. Moreover, the partition functions are determined by a gap condition combined with a simple recurrence relation which has its origins in a holomorphic anomaly that has been conjectured to exist for N = 4 topological Yang-Mills on manifolds with b + 2 = 1 and is also related to the holomorphic anomaly for higher genus topological strings on Calabi-Yau threefolds.