The Topological G2 String (original) (raw)
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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 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.
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.
From Topological Field Theories to Covariant Matrix Strings
Progress in String Theory and M-Theory, 2001
This paper is a shortened version of the previous work [2]: We propose a topological quantum field theory as a twisted candidate to formulate covariant matrix strings. The model relies on the octonionic or complexified instanton equations defined on an eight dimensional manifold with reduced holonomy. To allow untwisting of the model without producing an anomaly, we suggest (partially twisted) W-gravity as an "extended" 2d-gravity sector.
N = 2 string as a topological conformal theory
Physics Letters B, 1992
We prove that critical and subcritical N = 2 string theory gives a realization of an N = 2 superfield extension of the topological conformal algebra. The essential observation is the vanishing of the background ghost charge.
Supergravity and the knitting of the Kalb–Ramond two-form in eight-dimensional topological gravity
Physics Letters B, 2003
Topological euclidean gravity is built in eight dimensions for manifolds with Spin(7) ⊂ SO(8) holonomy. In a previous work, we considered the construction of an eight-dimensional topological theory describing the graviton and one graviphoton. Here we solve the question of determining a topological model for the combined system of a metric and a Kalb-Ramond two-form gauge field. We then recover the complete N = 1, D = 8 supergravity theory in a twisted form. We observe that the generalized self-duality conditions of our model correspond to the octonionic string equations.
cM < 1 string theory as a constrained topological sigma model
Physics Letters B, 1995
It has been argued by Ishikawa and Kato that by making use of a specific bosonization, c M = 1 string theory can be regarded as a constrained topological sigma model. We generalize their construction for any (p, q) minimal model coupled to two dimensional (2d) gravity and show that the energy-momentum tensor and the topological charge of a constrained topological sigma model can be mapped to the energy-momentum tensor and the BRST charge of c M < 1 string theory at zero cosmological constant. We systematically study the physical state spectrum of this topological sigma model and recover the spectrum in the absolute cohomology of c M < 1 string theory. This procedure provides us a manifestly topological representation of the continuum Liouville formulation of c M < 1 string theory.
Large N 2D Yang-Mills Theory and Topological String Theory
Communications in Mathematical Physics, 1997
We describe a topological string theory which reproduces many aspects of the 1/N expansion of SU (N) Yang-Mills theory in two spacetime dimensions in the zero coupling (A = 0) limit. The string theory is a modified version of topological gravity coupled to a topological sigma model with spacetime as target. The derivation of the string theory relies on a new interpretation of Gross and Taylor's "Ω −1 points." We describe how inclusion of the area, coupling of chiral sectors, and Wilson loop expectation values can be incorporated in the topological string approach.