String Field Theory Research Articles

Singularities and dualities of pedal curves in pseudo-hyperbolic and de Sitter space

For the spherical unit speed nonlightlike curve in pseudo-hyperbolic space and de Sitter space [Formula: see text] and a given point P, we can define naturally the pedal curve of [Formula: see text] relative to the pedal point P. When the pseudo-sphere dual curve germs are nonsingular, singularity types of such pedal curves depend only on locations of pedal points. In this paper, we give a complete list of normal forms for singularities and locations of pedal points when the pseudo-sphere dual curve germs are nonsingular. Furthermore, we obtain the extension results in dualities, which has wide influence on the open and closed string field theory and string dynamics in physics, and can be used to better solve the dynamics of trajectory particle condensation process.

Inflation in string field theory

In this paper, we analyze the inflationary cosmology using string field theory. This is done by using the zero level contribution from string field theory, which is a non-local tachyonic action. We will use the non-local Friedmann equations for this model based on string field theory, and calculate the slow-roll parameters for this model. We will then explicitly obtain the scalar and tensorial power spectrum, their related indices, and the tensor-to-scalar ratio for this model. Finally, we use cosmological data from Planck 2013 to 2018 to constrain the free parameters in this model, and find that string field theory is compatible with them.

Classical algebraic structures in string theory effective actions

We study generic properties of string theory effective actions obtained by classically integrating out massive excitations from string field theories based on cyclic homotopy algebras of A∞ or L∞ type. We construct observables in the UV theory and we discuss their fate after integration-out. Furthermore, we discuss how to compose two subsequent integrations of degrees of freedom (horizontal composition) and how to integrate out degrees of freedom after deforming the UV theory with a new consistent interaction (vertical decomposition). We then apply our general results to the open bosonic string using Witten’s open string field theory. There we show how the horizontal composition can be used to systematically integrate out the Nakanishi-Lautrup field from the set of massless excitations, ending with a non-abelian A∞-gauge theory for just the open string gluon. Moreover we show how the vertical decomposition can be used to construct effective open-closed couplings by deforming Witten OSFT with a tadpole given by the Ellwood invariant. Also, we discuss how the effective theory controls the possibility of removing the tadpole in the microscopic theory, giving a new framework for studying D-brane deformations induced by changes in the closed string background.

Optical solitons of fractional complex Ginzburg\u2013Landau equation with conformable, beta, and M-truncated derivatives: a comparative study

In this paper, we investigate the optical solitons of the fractional complex Ginzburg–Landau equation (CGLE) with Kerr law nonlinearity which shows various phenomena in physics like nonlinear waves, second-order phase transition, superconductivity, superfluidity, liquid crystals, and strings in field theory. A comparative approach is practised between the three suggested definitions of derivative viz. conformable, beta, and M-truncated. We have constructed the optical solitons of the considered model with a new extended direct algebraic scheme. By utilization of this technique, obtained solutions carry a variety of new families including dark-bright, dark, dark-singular, and singular solutions of Type 1 and 2, and sufficient conditions for the existence of these structures are given. Further, graphical representations of the obtained solutions are depicted. A detailed comparison of solutions to the considered problem, obtained by using different definitions of derivatives, is reported as well.

D-instanton perturbation theory

D-instanton world-volume theory has open string zero modes describing collective coordinates of the instanton. The usual perturbative amplitudes in the D-instanton background suffer from infra-red divergences due to the presence of these zero modes, and the usual approach of analytic continuation in momenta does not work since all open string states on a D-instanton carry strictly zero momentum. String field theory is well-suited for tackling these issues. However we find a new subtlety due to the existence of additional zero modes in the ghost sector. This causes a breakdown of the Siegel gauge, but a different gauge fixing consistent with the BV formalism renders the perturbation theory finite and unambiguous. At each order, this produces extra contribution to the amplitude besides what is obtained from integration over the moduli space of Riemann surfaces.

Open-closed hyperbolic string vertices

We construct a family of hyperbolic string vertices in the oriented open-closed string field theory, generalizing the recent result on hyperbolic closed string vertices by Costello and Zwiebach. The vertices are described by certain bordered hyperbolic surfaces and we explain relevant collar theorems which provide restrictions on the systolic conditions for the hyperbolic vertices. We also give explicit descriptions of the vertices for all zero and one-dimensional moduli spaces.

Three-point functions at strong coupling in the BMN limit

We consider structure constants of single-trace operators at strong coupling in planar mathcal{N} = 4 SYM theory using the hexagon formalism. We concentrate on heavy-heavy- light correlators where the heavy operators are BMN operators, with large R-charges and finite anomalous dimensions, and the light one is a finite-charge chiral primary operator. They describe the couplings between two highly boosted strings and a supergravity mode in the bulk dual. In the hexagon framework, two sums over virtual magnons are needed to bind the hexagons together around the light operator. We evaluate these sums explicitly at strong coupling, for a certain choice of BMN operators, and show that they factorise into a ratio of Gamma functions and a simple stringy prefactor. The former originates from giant mirror magnons scanning the AdS geometry while the latter stems from small fluctuations around the BMN vacuum. The resulting structure constants have poles at positions where an enhanced mixing with double-trace operators is expected and zeros whenever the process is forbidden by supersymmetry. We also discuss the transition to the classical regime, when the length of the light operator scales like the string tension, where we observe similitudes with the Neumann coefficients of the pp-wave String Field Theory vertex.

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 can support fluctuations provided they are “hidden” as nonperturbative effects behind a pure gauge asymptotic series.

Canonical quantization of massive symmetric rank-two tensor in string theory

The canonical quantization of a massive symmetric rank-two tensor in string theory, which contains two Stueckelberg fields, was studied. As a preliminary study, we performed a canonical quantization of the Proca model to describe a massive vector particle that shares common properties with the massive symmetric rank-two tensor model. By performing a canonical analysis of the Lagrangian, which describes the symmetric rank-two tensor, obtained by Siegel and Zwiebach (SZ) from string field theory, we deduced that the Lagrangian possesses only first class constraints that generate local gauge transformation. By explicit calculations, we show that the massive symmetric rank-two tensor theory is gauge invariant only in the critical dimension of open bosonic string theory, i.e., d=26. This emphasizes that the origin of local symmetry is the nilpotency of the Becchi-Rouet-Stora-Tyutin (BRST) operator, which is valid only in the critical dimension. For a particular gauge imposed on the Stueckelberg fields, the gauge-invariant Lagrangian of the SZ model reduces to the Fierz-Pauli Lagrangian of a massive spin-two particle. Thus, the Fierz-Pauli Lagrangian is a gauge-fixed version of the gauge-invariant Lagrangian for a massive symmetric rank-two tensor. By noting that the Fierz-Pauli Lagrangian is not suitable for studying massive spin-two particles with small masses, we propose the transverse-traceless (TT) gauge to quantize the SZ model as an alternative gauge condition. In the TT gauge, the two Stueckelberg fields can be decoupled from the symmetric rank-two tensor and integrated trivially. The massive spin-two particle can be described by the SZ model in the TT gauge, where the propagator of the massive spin-two particle has a well-defined massless limit.

Convex Programs for Minimal-Area Problems

The minimal-area problem that defines string diagrams in closed string field theory asks for the metric of least area on a Riemann surface with the condition that all non-contractible closed curves have length at least \(2\pi \). 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.

Minimal-Area Metrics on the Swiss Cross and Punctured Torus

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 2\pi. Through every point in such a metric there is a geodesic that saturates the length condition, and saturating geodesics in a given homotopy class form a band. The extremal metric is unknown when bands of geodesics cross, as it happens for surfaces of non-zero genus. We use recently proposed convex programs to numerically find the minimal-area metric on the square torus with a square boundary, for various sizes of the boundary. For large enough boundary the problem is equivalent to the "Swiss cross" challenge posed by Strebel. We find that the metric is positively curved in the two-band region and flat in the single-band regions. For small boundary the metric develops a third band of geodesics wrapping around it, and has both regions of positive and negative curvature. This surface can be completed to provide the minimal-area metric on a once-punctured torus, representing a closed-string tadpole diagram.

Type II superstring field theory with cyclic $L_\infty$ structure

Abstract We construct a complete type II superstring field theory that includes all the NS–NS, R–NS, NS–R, and R–R sectors. As in the open and heterotic superstring cases, the R–NS, NS–R, and R–R string fields are constrained by using the picture-changing operators. In particular, we use a non-local inverse picture-changing operator for the constraint on the R–R string field, which seems to be inevitable due to the compatibility of the extra constraint with the closed string constraints. The natural symplectic form in the restricted Hilbert space gives a non-local kinetic action for the R–R sector, but it correctly provides the propagator expected from the first-quantized formulation. Extending the prescription previously obtained for the heterotic string field theory, we give a construction of general type II superstring products, which realizes a cyclic $L_\infty$ structure, and thus provides a gauge-invariant action based on the homotopy algebraic formulation. Three typical four-string amplitudes derived from the constructed string field theory are demonstrated to agree with those in the first-quantized formulation. We also give the half-Wess–Zumino–Witten action defined in the medium Hilbert space whose left-moving sector is still restricted to the small Hilbert space.

Fixing an ambiguity in two dimensional string theory using string field theory

In a recent paper, Balthazar, Rodriguez and Yin found some remarkable agreement between the results of c = 1 matrix model and D-instanton corrections in two dimensional string theory. Their analysis left undetermined two constants in the string theory computation which had to be fixed by comparing the results with the matrix model results. One of these constants is affected by possible renormalization of the D-instanton action that needs to be computed separately. In this paper we fix the other constant by reformulating the world-sheet analysis in the language of string field theory.

Pictures from super Chern-Simons theory

We study super-Chern-Simons theory on a generic supermanifold. After a self-contained review of integration on supermanifolds, the complexes of forms (superforms, pseudoforms and integral forms) and the extended Cartan calculus are discussed. We then introduce Picture Changing Operators and their mathematical properties. We show that the free equations of motion reduce to the usual Chern-Simons equations proving on-shell equivalence between the formulations at different pictures of the same theory. Finally, we discuss the interaction terms. They require a suitable definition in order to take into account the picture number. This leads to the construction of a series of non-associative products which yield an A∞ algebra structure, sharing several similarities with the super string field theory action by Erler, Konopka and Sachs.

Supersymmetry in the time domain and its applications in optics

Supersymmetry is a conjectured symmetry between bosons and fermions aiming at solving fundamental questions in string and quantum field theory. Its subsequent application to quantum mechanics led to a ground-breaking analysis and design machinery, later fruitfully extrapolated to photonics. In all cases, the algebraic transformations of quantum-mechanical supersymmetry were conceived in the space realm. Here, we demonstrate that Maxwell’s equations, as well as the acoustic and elastic wave equations, also possess an underlying supersymmetry in the time domain. We explore the consequences of this property in the field of optics, obtaining a simple analytic relation between the scattering coefficients of numerous time-varying systems, and uncovering a wide class of reflectionless, three dimensional, all-dielectric, isotropic, omnidirectional, polarisation-independent, non-complex media. Temporal supersymmetry is also shown to arise in dispersive media supporting temporal bound states, which allows engineering their momentum spectra and dispersive properties. These unprecedented features may enable the creation of novel reconfigurable devices, including invisible materials, frequency shifters, isolators, and pulse-shape transformers.

Localization of effective actions in heterotic string field theory

We consider the algebraic couplings in the tree level effective action of the heterotic string. We show how these couplings can be computed from closed string field theory. When the light fields we are interested in are charged under an underlying mathcal{N} = 2 R-charge in the left-moving sector, their quartic effective potential localizes at the boundary of the worldsheet moduli space, in complete analogy to the previously studied open string case. In particular we are able to compute the quartic closed string field theory potential without resorting to any explicit expression for the 3- and the 4-strings vertices but only using the L∞ relations between them. As a non trivial example we show how the heterotic Yang-Mills quartic potential arises in this way.

Four lectures on closed string field theory

The following notes derive from review lectures on closed string field theory given at the Galileo Galilei Institute for Theoretical Physics in March 2019.

String field theory solution for any open string background. Part 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.

Heterotic string field theory with cyclic L∞ structure

A correction has been published:Progress of Theoretical and Experimental Physics, Volume 2020, Issue 1, January 2020, 019201, https://doi.org/10.1093/ptep/ptz148.

Homotopy algebras in higher spin theory

Motivated by string field theory, we explore various algebraic aspects of higher spin theory and Vasiliev equation in terms of homotopy algebras. We present a systematic study of unfolded formulation developed for the higher spin equation in terms of the Maurer-Cartan equation associated to differential forms valued in L-infinity algebras. The elimination of auxiliary variables of Vasiliev equation is analyzed through homological perturbation theory. This leads to a closed combinatorial graph formula for all the vertices of higher spin equations in the unfolded formulation. We also discover a topological quantum mechanics model whose correlation functions give deformed higher spin vertices at first order.