arXiv subjects

Atakan Hilmi Fırat

Publications and source records attributed to Atakan Hilmi Fırat.

At least 19 recordsLinked to original sources

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

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 Poincaré 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

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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arXiv2026

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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arXiv2026

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

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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arXiv2025

Boundary terms in string field theory

We supplement the string field theory action with boundary terms to make its variational principle well-posed. Central to our considerations is the violation of the stress-energy tensor conservation in non-compact CFTs due to the boundary terms. This manifests as the failure of the cyclicity of the BRST operator, which encodes the target space integration by parts identities at the level of the worldsheet. Using this failure, we argue that the free closed string field theory action admits a well-posed variational principle upon including an additional boundary contribution. We explicitly work out the resulting action up to the massless level and show that it is related to the expansion of the low-energy effective string action endowed with the Gibbons-Hawking-York term on a flat background. We also discuss the structure of the boundary terms in the interacting theory.

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arXiv2024

Topological recursion for hyperbolic string field theory

We derive an analog of Mirzakhani's recursion relation for hyperbolic string vertices and investigate its implications for closed string field theory. Central to our construction are systolic volumes: the Weil-Petersson volumes of regions in moduli spaces of Riemann surfaces whose elements have systoles $L \geq 0$. These volumes can be shown to satisfy a recursion relation through a modification of Mirzakhani's recursion as long as $L \leq 2 \sinh^{-1} 1$. Applying the pants decomposition of Riemann surfaces to off-shell string amplitudes, we promote this recursion to hyperbolic string field theory and demonstrate the higher order vertices are determined by the cubic vertex iteratively for any background. Such structure implies the solutions of closed string field theory obey a quadratic integral equation. We illustrate the utility of our approach in an example of a stubbed scalar theory.

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arXiv2024

$A_\infty$ perspective to Sen's formalism

Sen's formalism is a mechanism for eliminating constraints on the dynamical fields that are imposed independently from equations of motion by employing spurious free fields. In this note a cyclic homotopy associative algebra underlying Sen's formalism is developed. The novelty lies in the construction of a symplectic form and cyclic $A_\infty$ maps on an extended algebra that combines the dynamical and spurious fields. This algebraic presentation makes the gauge invariance of theories using Sen's formulation manifest.

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arXiv2024

Open string stub as an auxiliary string field

Witten's open string field theory with a generalized version of stubs is reformulated as a cubic string field theory using an auxiliary string field. The gauge symmetries and equations of motion as well as the associative algebra of the resulting theory are investigated. Integrating out either the original or auxiliary field is shown to recover the conventional cubic theory. Our analysis demonstrates that deformations due to the stubs can be described as a homotopy transfer purely in the context of strong deformation retract. We also discuss to what extent the vertex regions resulting from stubs provide a model for the elementary interactions of closed string field theory.

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arXiv2023

Hyperbolic string tadpole

Hyperbolic geometry on the one-bordered torus is numerically uniformized using Liouville theory. This geometry is relevant for the hyperbolic string tadpole vertex describing the one-loop quantum corrections of closed string field theory. We argue that the Lamé equation, upon fixing its accessory parameter via Polyakov conjecture, provides the input for the characterization. The explicit expressions for the Weil-Petersson metric as well as the local coordinates and the associated vertex region for the tadpole vertex are given in terms of classical torus conformal blocks. The relevance of this vertex for vacuum shift computations in string theory is highlighted.

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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 Padé 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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arXiv2023

String vertices for the large $N$ limit

String vertices of open-closed string field theory on an arbitrary closed string background with $N$ identical D-branes are investigated when $N$ is large. We identify the relevant geometric master equation and solve it using open-closed hyperbolic genus zero string vertices with a milder systolic constraint. The limits corresponding to integrating out open or closed strings are investigated. We highlight the possible implications of our construction to AdS/CFT correspondence.

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arXiv2023

Bootstrapping closed string field theory

The determination of the string vertices of closed string field theory is shown to be a conformal field theory problem solvable by combining insights from Liouville theory, hyperbolic geometry, and conformal bootstrap. We first demonstrate how Strebel differentials arise from hyperbolic string vertices by performing a WKB approximation to the associated Fuchsian equation, which we subsequently use it to derive a Polyakov-like conjecture for Strebel differentials. This result implies that the string vertices are generated by the interactions of $n$ zero momentum tachyons, or equivalently, a certain limit of suitably regularized on-shell Liouville action. We argue that the latter can be related to the interaction of three zero momentum tachyons on a generalized cubic vertex through classical conformal blocks. We test this claim for the quartic vertex and discuss its generalization to higher-string interactions.

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arXiv2022

Characterizing 4-string contact interaction using machine learning

The geometry of 4-string contact interaction of closed string field theory is characterized using machine learning. We obtain Strebel quadratic differentials on 4-punctured spheres as a neural network by performing unsupervised learning with a custom-built loss function. This allows us to solve for local coordinates and compute their associated mapping radii numerically. We also train a neural network distinguishing vertex from Feynman region. As a check, 4-tachyon contact term in the tachyon potential is computed and a good agreement with the results in the literature is observed. We argue that our algorithm is manifestly independent of number of punctures and scaling it to characterize the geometry of $n$-string contact interaction is feasible.

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arXiv2022

D-instanton Induced Superpotential

We use string field theory to fix the normalization of the D-instanton corrections to the superpotential involving the moduli fields of type II string theory compactified on an orientifold of a Calabi-Yau threefold in the absence of fluxes. We focus on $O(1)$ instantons whose only zero modes are the four bosonic modes associated with translation of the instanton in non-compact directions and a pair of fermionic zero modes associated with the two supercharges broken by the instanton. We work with a generic superconformal field theory and express our answer in terms of the spectrum of open strings on the instanton. We analyse the contribution of multi-instantons of this kind to the superpotential and argue that it vanishes when background fluxes are absent.

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arXiv2021

Initial value problem in string-inspired nonlocal field theory

We consider a nonlocal scalar field theory inspired by the tachyon action in open string field theory. The Lorentz-covariant action is characterized by a parameter $ξ^2$ that quantifies the amount of nonlocality. Restricting to purely time-dependent configurations, we show that a field redefinition perturbative in $ξ^2$ reduces the action to a local two-derivative theory with a $ξ^2$-dependent potential. This picture is supported by evidence that the redefinition maps the wildly oscillating rolling tachyon solutions of the nonlocal theory to conventional rolling in the new scalar potential. For general field configurations we exhibit an obstruction to a local Lorentz-covariant formulation, but we can still achieve a formulation local in time, as well as a light-cone formulation. These constructions provide an initial value formulation and a Hamiltonian. Their causality is consistent with a lack of superluminal behavior in the nonlocal theory.

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