Hyperbolic geometry and closed bosonic string field theory. Part I. The string vertices via hyperbolic Riemann surfaces

Moosavian, Seyed Faroogh; Pius, Roji

doi:10.1007/jhep08(2019)157

Cited by 36 publications

(55 citation statements)

References 67 publications

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“…For example if we use hyperbolic metric to introduce the local coordinate system as in[39][40][41] then the subspaces C(1) s 's will be obtained by setting to some small number ℓ 0 the length of the closed geodesic that shrinks to a point at the s-th degeneration of the punctured sphere. Similar regularization was used in[42] for computing tree level string amplitudes with large number of external states, but only the C (0) I (0) contribution was analyzed in[42].…”

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confidence: 99%

String field theory as world-sheet UV regulator

Sen

2019

J. High Energ. Phys.

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Even at tree level, the first quantized string theory suffers from apparent short distance singularities associated with collision of vertex operators that prevent us from straightforward numerical computation of various quantities. Examples include string theory S-matrix for generic external momenta and computation of the spectrum of string theory under a marginal deformation of the world-sheet theory. The former requires us to define the S-matrix via analytic continuation or as limits of contour integrals in complexified moduli space, while the latter requires us to use an ultraviolet cut-off at intermediate steps. In contrast, string field theory does not suffer from such divergences. In this paper we show how string field theory can be used to generate an explicit algorithm for computing tree level amplitudes in any string theory that does not suffer from any short distance divergence from integration over the worldsheet variables. We also use string field theory to compute second order mass shift of string states under a marginal deformation without having to use any cut-off at intermediate steps.We carry out the analysis in a broad class of string field theories, thereby making it manifest that the final results are independent of the extra data that go into the formulation of string field theory. We also comment on the generalization of this analysis to higher genus amplitudes.

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confidence: 99%

String field theory as world-sheet UV regulator

Sen

2019

J. High Energ. Phys.

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“…The construction is not without some (weak) mathematical assumptions and may require an adjustment of the propagator at each order of perturbation theory. Another option, recently investigated by Moosavian and Pius [29], is to use hyperbolic metrics. There is an obvious challenge here: hyperbolic metrics are not consistent with sewing.…”

Section: Figurementioning

confidence: 99%

Convex Programs for Minimal-Area Problems

Headrick

Zwiebach

2020

Commun. Math. Phys.

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The closed string field theory minimal-area problem asks for the conformal metric of least area on a Riemann surface with the condition that all non-contractible closed curves have length at least 2π. This is an extremal length problem in conformal geometry as well as a problem in systolic geometry. We consider the analogous minimal-area problem for homology classes of curves and, with the aid of calibrations and the max flow-min cut theorem, formulate it as a local convex program. We derive an equivalent dual program involving maximization of a concave functional. These two programs give new insights into the form of the minimal-area metric and are amenable to numerical solution. We explain how the homology problem can be modified to provide the solution to the original homotopy problem.

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“…Our basic premise is to start with the picture we have described for the Chern-Simons 11 See [62][63][64] for discussions of the physical closed string field theory.…”

Section: Entanglement In Closed Topological String Theorymentioning

confidence: 99%

Topological string entanglement

Hubeny

Pius

Rangamani

2019

J. High Energ. Phys.

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We investigate how topological entanglement of Chern-Simons theory is captured in a string theoretic realization. Our explorations are motivated by a desire to understand how quantum entanglement of low energy open string degrees of freedom is encoded in string theory (beyond the oft discussed classical gravity limit). Concretely, we realize the Chern-Simons theory as the worldvolume dynamics of topological D-branes in the topological A-model string theory on a Calabi-Yau target. Via the open/closed topological string duality one can map this theory onto a pure closed topological A-model string on a different target space, one which is related to the original Calabi-Yau geometry by a geometric/conifold transition. We demonstrate how to uplift the replica construction of Chern-Simons theory directly onto the closed string and show that it provides a meaningful definition of reduced density matrices in topological string theory. Furthermore, we argue that the replica construction commutes with the geometric transition, thereby providing an explicit closed string dual for computing reduced states, and Rényi and von Neumann entropies thereof. While most of our analysis is carried out for Chern-Simons on S 3 , the emergent picture is rather general. Specifically, we argue that quantum entanglement on the open string side is mapped onto quantum entanglement on the closed string side and briefly comment on the implications of our result for physical holographic theories where entanglement has been argued to be crucial ingredient for the emergence of classical geometry. A The Topology of the Conifold 50 B Normalized Chern-Simons density matrices 53 C Chern-Simons and topological string observables 57 C.1 Chern-Simons partition sums 57 C.2 Wilson loop generating functions 58 D Brief Review of Topological String Theory 59 -1 -Combining the equations (4.3) and (4.4) and accounting for our normalization choice we learn

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Hyperbolic geometry and closed bosonic string field theory. Part I. The string vertices via hyperbolic Riemann surfaces

Cited by 36 publications

References 67 publications

String field theory as world-sheet UV regulator

String field theory as world-sheet UV regulator

Convex Programs for Minimal-Area Problems

Topological string entanglement

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