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Theodore Erler

Publications and source records attributed to Theodore Erler.

At least 37 records · Page 2Linked to original sources
arXiv2017

Superstring Field Theory and the Wess-Zumino-Witten Action

We describe a notion of "higher" Wess-Zumino-Witten-like action which is natural in the context of superstring field theories formulated in the large Hilbert space. For the open string, the action is characterized by a pair of commuting cyclic $A_\infty$ structures together with a hierarchy of higher-form potentials analogous to the Maurer-Cartan elements which appear in the conventional Wess-Zumino-Witten action. We apply this formalism to get a better understanding of symmetries of open superstring field theory and the structure of interactions in the Ramond sector, describing an interesting connection between Ramond vertices and Feynman diagrams.

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arXiv2016

Supersymmetry in Open Superstring Field Theory

We realize the 16 unbroken supersymmetries on a BPS D-brane as invariances of the action of the corresponding open superstring field theory. We work in the small Hilbert space approach, where a symmetry of the action translates into a symmetry of the associated cyclic $A_\infty$ structure. We compute the supersymmetry algebra, being careful to disentangle the components which produce a translation, a gauge transformation, and a symmetry transformation which vanishes on-shell. Via the minimal model theorem, we illustrate how supersymmetry of the action implies supersymmetry of the tree level open string scattering amplitudes.

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arXiv2016

Complete Action for Open Superstring Field Theory with Cyclic $A_\infty$ Structure

We construct a gauge invariant action for the Neveu-Schwarz and Ramond sectors of open superstring field theory realizing a cyclic $A_\infty$ structure, providing the first complete and fully explicit solution to the classical Batalin-Vilkovisky master equation in superstring field theory. We also demonstrate the equivalence of our action to the Wess-Zumino-Witten-based construction of Kunitomo and one of the authors.

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arXiv2016

Relating Berkovits and $A_\infty$ Superstring Field Theories; Small Hilbert Space Perspective

In a previous paper it was shown that the recently constructed action for open superstring field theory based on $A_\infty$ algebras can be re-written in Wess-Zumino-Witten-like form, thus establishing its relation to Berkovits' open superstring field theory. In this paper we explain the relation between these two theories from a different perspective which emphasizes the small Hilbert space, and in particular the relation between the $A_\infty$ structures on both sides.

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arXiv2015

Relating Berkovits and $A_\infty$ Superstring Field Theories; Large Hilbert Space Perspective

We lift the dynamical field of the $A_\infty$ superstring field theory to the large Hilbert space by introducing a gauge invariance associated with the eta zero mode. We then provide a field redefinition which relates the lifted field to the dynamical field of Berkovits' superstring field theory in the large Hilbert space. This generalizes the field redefinition in the small Hilbert space described in earlier works, and gives some understanding of the relation between the gauge symmetries of the theories. It also provides a new perspective on the algebraic structure underlying gauge invariance of the Wess-Zumino-Witten-like action.

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arXiv2015

Ramond Equations of Motion in Superstring Field Theory

We extend the recently constructed NS superstring field theories in the small Hilbert space to give classical field equations for all superstring theories, including Ramond sectors. We also comment on the realization of supersymmetry in this framework.

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arXiv2015

$A_\infty$ structure from the Berkovits formulation of open superstring field theory

By formulating open superstring field theory based on the small Hilbert space of the superconformal ghost sector, an action for the Neveu-Schwarz sector with an $A_\infty$ structure has recently been constructed. We transform this action to the Wess-Zumino-Witten-like form and show that this theory is related to the Berkovits formulation of open superstring field theory based on the large Hilbert space by partial gauge fixing and field redefinition.

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arXiv2014

String Field Theory Solution for Any Open String Background

We present an exact solution of open bosonic string field theory which can be used to describe any time-independent open string background. The solution generalizes an earlier construction of Kiermaier, Okawa, and Soler, and assumes the existence of boundary condition changing operators with nonsingular OPEs and vanishing conformal dimension. Our main observation is that boundary condition changing operators of this kind can describe nearly any open string background provided the background shift is accompanied by a timelike Wilson line of sufficient strength. As an application we analyze the tachyon lump describing the formation of a D$(p-1)$-brane in the string field theory of a D$p$-brane, for generic compactification radius. This not only provides a proof of Sen's second conjecture, but also gives explicit examples of higher energy solutions, confirming analytically that string field theory can "reverse" the direction of the worldsheet RG flow. We also find multiple D-brane solutions, demonstrating that string field theory can add Chan-Paton factors and change the rank of the gauge group. Finally, we show how the solution provides a remarkably simple and nonperturbative proof of the background independence of open bosonic string field theory.

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arXiv2014

NS-NS Sector of Closed Superstring Field Theory

We give a construction for a general class of vertices in superstring field theory which include integration over bosonic moduli as well as the required picture changing insertions. We apply this procedure to find a covariant action for the NS-NS sector of Type II closed superstring field theory.

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arXiv2013

Resolving Witten's Superstring Field Theory

We regulate Witten's open superstring field theory by replacing the picture-changing insertion at the midpoint with a contour integral of picture changing insertions over the half-string overlaps of the cubic vertex. The resulting product between string fields is non-associative, but we provide a solution to the $A_\infty$ relations defining all higher vertices. The result is an explicit covariant superstring field theory which by construction satisfies the classical BV master equation.

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arXiv2013

Analytic Solution for Tachyon Condensation in Berkovits' Open Superstring Field Theory

We present an analytic solution for tachyon condensation on a non-BPS D-brane in Berkovits' open superstring field theory. The solution is presented as a product of $2\times 2$ matrices in two distinct $GL_2$ subgroups of the open string star algebra. All string fields needed for computation of the nonpolynomial action can be derived in closed form, and the action produces the expected non-BPS D-brane tension in accordance with Sen's conjecture. We also comment on how D-brane charges may be encoded in the topology of the tachyon vacuum gauge orbit.

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arXiv2012

Connecting Solutions in Open String Field Theory with Singular Gauge Transformations

We show that any pair of classical solutions of open string field theory can be related by a formal gauge transformation defined by a gauge parameter $U$ without an inverse. We investigate how this observation can be used to construct new solutions. We find that a choice of gauge parameter consistently generates a new solution only if the BRST charge maps the image of $U$ into itself. When this occurs, we argue that $U$ naturally defines a star algebra projector which describes a surface of string connecting the boundary conformal field theories of the classical solutions related by $U$. We also note that singular gauge transformations give the solution space of open string field theory the structure of a category, and we comment on the physical interpretation of this observation.

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arXiv2012

The Phantom Term in Open String Field Theory

We show that given any two classical solutions in open string field theory and a singular gauge transformation relating them, it is possible to write the second solution as a gauge transformation of the first plus a singular, projector-like state which describes the shift in the open string background between the two solutions. This is the "phantom term." We give some applications in the computation of gauge invariant observables.

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arXiv2011

Comments on Lumps from RG flows

In this note we investigate the proposal of Ellwood and one of the authors et al. to construct a string field theory solution describing the endpoint of an RG flow from a reference BCFT to a target BCFT*. We show that the proposed class of solutions suffers from an anomaly in the equations of motion. Nevertheless, the gauge invariant action exactly reproduces the expected shift in energy.

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arXiv2011

Exotic Universal Solutions in Cubic Superstring Field Theory

We present a class of analytic solutions of cubic superstring field theory in the universal sector on a non-BPS D-brane. Computation of the action and gauge invariant overlap reveal that the solutions carry half the tension of a non-BPS D-brane. However, the solutions do not satisfy the reality condition. In fact, they display an intriguing topological structure: We find evidence that conjugation of the solutions is equivalent to a gauge transformation that cannot be continuously deformed to the identity.

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arXiv2009

A Simple Analytic Solution for Tachyon Condensation

In this paper we present a new and simple analytic solution for tachyon condensation in open bosonic string field theory. Unlike the B_0 gauge solution, which requires a carefully regulated discrete sum of wedge states subtracted against a mysterious "phantom" counter term, this new solution involves a continuous integral of wedge states, and no regularization or phantom term is necessary. Moreover, we can evaluate the action and prove Sen's conjecture in a mere few lines of calculation.

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arXiv2007

Split String Formalism and the Closed String Vacuum

The split string formalism offers a simple template upon which we can build many generalizations of Schnabl's analytic solution of open string field theory. In this paper we consider two such generalizations: one which replaces the wedge state by an arbitrary function of wedge states, and another which generalizes the solution to conformal frames other than the sliver.

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