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Theodore Erler

Publications and source records attributed to Theodore Erler.

At least 19 recordsLinked to original sources
arXiv2026

Poisson bracket and $L_\infty$ algebras

We describe the Poisson bracket of a Lagrangian field theory expressed in the framework of $L_\infty$ algebras. If the symplectic structure on phase space is defined following recent work, we show that the Poisson bracket can be computed with the Peierls formula, confirming the well-known result of the covariant phase space formalism. Of particular interest is the Poisson bracket in nonlocal theories. In $p$-adic string theory we find that a straightforward construction of the Poisson bracket is obstructed by higher derivative instabilities. We also discuss the inverse relation between the Poisson bracket and symplectic structure in the language of homological algebra, extending some ideas in the mathematical physics literature.

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arXiv2026

D-brane tension as central charge

Using Hamiltonian methods in open bosonic string field theory, we derive the mass of a D0-brane as the central charge of the spontaneously broken Poincar\'e algebra in 26 dimensions. Though the formulas originate from string field theory, the calculation can be carried out completely on-shell. This illustrates a general procedure for computing spacetime central charges in string theory.

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arXiv2026

Conserved charges and $L_\infty$ algebras

We give a formula for conserved charges in an arbitrary Lagrangian field theory expressed in the framework of $L_\infty$ algebras. The formula is determined by the theory's $L_\infty$ data alone, without reference to the derivative structure of the Lagrangian. Therefore conserved charges can be computed in nonlocal models, such as string field theory, where conventional methods break down. The formula also gives the correct expression for the Hamiltonian of general relativity as a surface integral of the Brown-York stress tensor. Related computations in Yang-Mills theory suggest that spatial boundaries are dealt with in a natural fashion.

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arXiv2026

Symplectic structure in open string field theory III: Electric field

We use a new formula for the symplectic structure on the phase space of open string field theory to evaluate the energy of a D-brane carrying a constant electric flux. This is shown to be consistent with the energy computed using the Dirac-Born-Infeld action through a generalization of the Ellwood invariant to nonpolynomial open string field theories.

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arXiv2025

Symplectic structure in open string field theory II: Sliding lump

We use a new formula for symplectic structure to compute the momentum of an analytic lump solution moving at constant velocity in Witten's open string field theory. The computation gives a new way to determine the D-brane tension in string field theory. Using homotopy algebra technology, we prove that this tension must agree with the value implied by the on-shell action.

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arXiv2025

Symplectic structure in open string field theory I: Rolling tachyons

We discuss a new formula for the symplectic structure on the phase space of open string field theory. Revisiting the setup of Cho, Mazel, and Yin, we use the formula to compute the energy of rolling tachyon solutions on unstable D-branes. An important aspect of the analysis is dealing with the singular ultraviolet behavior of string vertices in Lorentzian signature, a feature we refer to as transgressive locality. This forces us to carry out computations in momentum space, where time and causality are somewhat obscure. Nevertheless the symplectic structure appears to be sensible, giving results in agreement with boundary state computations. As further confirmation of our methods, we study the symplectic structure for rolling tachyons in scalar effective field theory, where vertices show similar high energy behavior to string field theory but the physics is that of local field theory. This model gives interesting insight into the runaway oscillations of the rolling tachyon.

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arXiv2025

Covariant phase space and $L_\infty$ algebras

We propose a symplectic structure for the phase space of a generic Lagrangian field theory expressed in the framework of $L_\infty$ algebras. The symplectic structure does not require explicit knowledge of the derivative content of the Lagrangian, and therefore is applicable to nonlocal models, such as string field theory, where traditional constructions are difficult to apply. We test our proposal in a number of examples ranging from general relativity to $p$-adic string theory.

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arXiv2024

Open string field theory in lightcone gauge

We study covariant open bosonic string field theory in lightcone gauge. When lightcone gauge is well-defined, we find two results. First, the vertices of the gauge-fixed action consist of Mandelstam diagrams with stubs covering specific portions of the moduli spaces of Riemann surfaces. This is true regardless of how the vertices of the original covariant string field theory are constructed (e.g. through minimal area metrics, hyperbolic geometry, and so on). Second, the portions of moduli space covered by gauge-fixed vertices are changed relative to those covered by the original covariant vertices. The extra portions are supplied through the exchange of longitudinal degrees of freedom in scattering processes.

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arXiv2023

Wilsonian effective potentials and closed string field theory

We investigate Wilsonian effective field theory as a model for the construction of the tachyon potential and nonperturbative vacua in closed string field theory. In a number of cases we are able to find the effective potential exactly, and observe what appear to be universal features. We find that the effective field theory contains the same nonperturbative vacuum structure as the bare Lagrangian, though this information is encoded less efficiently as the distance scale of the effective field theory is increased. The implication is that closed string field theory plausibly contains information about the nonperturbative vacuum structure of string theory, in spite of its similarities to effective field theory. We also truncate the effective potential at a fixed power of the field and investigate how the global structure of the effective potential may be approximated via Pad\'e resummation. Qualitative comparisons suggest that computation of the eighth to sixteenth order closed string vertex should be enough to obtain reliable results for the closed string field theory action evaluated on the tachyon field.

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arXiv2021

Mapping between Witten and Lightcone String Field Theories

We propose a transformation between the off-shell field variables of Witten's open bosonic string field theory and the traditional lightcone string field theory of Kaku and Kikkawa, based on Mandelstam's interacting string picture. This is accomplished by deforming the Witten vertex into lightcone cubic and quartic vertices, followed by integrating out the ghost and lightcone oscillator excitations from the string field. Surprisingly, the last step does not alter the cubic and quartic interactions and does not generate effective vertices, and leads precisely to Kaku and Kikkawa's lightcone string field theory.

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arXiv2020

String Field Theory Solution for Any Open String Background. II

Generalizing previous work, we give a new analytic solution in Witten's open bosonic string field theory which can describe any open string background. The central idea is to use Riemann surface degenerations as a mechanism for taming OPE singularities. This requires leaving the familiar subalgebra of wedge states with insertions, but the payoff is that the solution makes no assumptions about the reference and target D-brane systems, and is therefore truly general. For example, unlike in previous work, the solution can describe time dependent backgrounds and multiple copies of the reference D-brane within the universal sector. The construction also resolves some subtle issues resulting from associativity anomalies, giving a more complete understanding of the relation between the degrees of freedom of different D-brane systems, and a nonperturbative proof of background independence in classical open bosonic string field theory.

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arXiv2019

Taming boundary condition changing operator anomalies with the tachyon vacuum

Motivated by the appearance of associativity anomalies in the context of superstring field theory, we give a generalized solution built from boundary condition changing operators which can be associated to a generic tachyon vacuum in the $KBc$ subalgebra of the Okawa form. We articulate sufficient conditions on the choice of tachyon vacuum to ensure that ambiguous products do not appear in the equations of motion.

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arXiv2019

Rolling Near the Tachyon Vacuum

In a linear dilaton background, it has been argued that an unstable D-brane can decay to the tachyon vacuum without leaving behind a remnant of tachyon matter. Here we address the question of how the D-brane can decay to the tachyon vacuum when the tachyon vacuum does not support physical fluctuations. Using the formalism of open string field theory, we find that the tachyon vacuum {\it can} support fluctuations provided they are "hidden" as nonperturbative effects behind a pure gauge asymptotic series.

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arXiv2017

Vertical Integration from the Large Hilbert Space

We develop an alternative description of the procedure of vertical integration based on the observation that amplitudes can be written in BRST exact form in the large Hilbert space. We relate this approach to the description of vertical integration given by Sen and Witten.

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arXiv2017

One Loop Tadpole in Heterotic String Field Theory

We compute the off-shell 1-loop tadpole amplitude in heterotic string field theory. With a special choice of cubic vertex, we show that this amplitude can be computed exactly. We obtain explicit and elementary expressions for the Feynman graph decomposition of the moduli space, the local coordinate map at the puncture as a function of the modulus, and the $b$-ghost insertions needed for the integration measure. Recently developed homotopy algebra methods provide a consistent configuration of picture changing operators. We discuss the consequences of spurious poles for the choice of picture changing operators.

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