String Field Theory Research Articles

Mean string field theory: Landau-Ginzburg theory for 1-form symmetries

By analogy with the Landau-Ginzburg theory of ordinary zero-form symmetries, we introduce and develop a Landau-Ginzburg theory of one-form global symmetries, which we call mean string field theory. The basic dynamical variable is a string field – defined on the space of closed loops – that can be used to describe the creation, annihilation, and condensation of effective strings. Like its zero-form cousin, the mean string field theory provides a useful picture of the phase diagram of broken and unbroken phases. We provide a transparent derivation of the area law for charged line operators in the unbroken phase and describe the dynamics of gapless Goldstone modes in the broken phase. The framework also provides a theory of topological defects of the broken phase and a description of the phase transition that should be valid above an upper critical dimension, which we discuss. We also discuss general consequences of emergent one-form symmetries at zero and finite temperature.

The classical cosmological constant of open-closed string field theory

We consider deformations of D-brane systems induced by a change in the closed string background in the framework of bosonic open-closed string field theory, where it is possible to unambiguously tame infrared divergences originating from both open and closed string degenerations. A closed string classical solution induces a tadpole for the open strings which shifts the open string vacuum and generates a cosmological constant composed of two terms: one which is directly related to the closed string solution and the other which depends on the open string vacuum shift. We show that only the sum of these two terms is invariant under closed SFT gauge transformations and therefore is an observable. We conjecture that this observable is universally proportional to the shift in the world-sheet disk partition function between the starting D-brane in undeformed background and the final D-brane in deformed background, which typically includes also a change in the string coupling constant. We test the conjecture by considering a perturbative closed string solution describing deformations of a Narain compactification and, from the SFT cosmological constant, we reproduce the expected shift in the g-function of various D-branes living in the compactification. In doing this we are also able to identify a surprising change in the string coupling constant at second order in the deformation.

The closed string field theory action vanishes

Using the dilaton theorem, we show that the classical action of closed string field theory vanishes on-shell.

Perturbative path-integral of string fields and the A∞ structure of the BV master equation

Abstract The perturbative path-integral gives a morphism of the (quantum) A∞ structure intrinsic to each quantum field theory, which we show explicitly on the basis of the homological perturbation. As is known, in the Batalin–Vilkovisky (BV) formalism, any effective action also solves the BV master equation, which implies that the path-integral can be understood as a morphism of the BV differential. Since each solution of the BV master equation is in one-to-one correspondence with a quantum A∞ structure, the path-integral preserves this intrinsic A∞ structure of quantum field theory, where A∞ reduces to L∞ whenever multiplications of space-time fields are graded commutative. We apply these ideas to string-field theory and (re-)derive some quantities based on the perturbative path-integral, such as effective theories with finite α′, reduction of gauge and unphysical degrees, the S-matrix, and gauge-invariant observables.

Unitarity and Low Energy Expansion of the Coon Amplitude.

The Coon amplitude is a deformation of the Veneziano amplitude with logarithmic Regge trajectories and an accumulation point in the spectrum, which interpolates between string theory and field theory. With string theory, it is the only other solution to duality constraints explicitly known and it constitutes an important data point in the modern S-matrix bootstrap. Yet, its basics properties are essentially unknown. In this Letter, we fill this gap and derive the conditions of positivity and the low energy expansion of the amplitude. On the positivity side, we discover that the amplitude switches from a regime where it is positive in all dimensions to a regime with critical dimensions, which connects to the known d=26, 10 when the deformation is removed. Incidentally, we find that the Veneziano amplitude can be extended to massive scalars of masses up to m^{2}=1/3, where it has critical dimension 6.3. On the low-energy side, we compute the first few couplings of the theory in terms of q-deformed analogs of the standard Riemann zeta values of the string expansion. We locate their location in the EFT-hedron, and find agreement with a recent conjecture that theories with accumulation points populate this space. We also discuss their relation to low spin dominance. Finally, we comment on the length of the Coon parton.

Generating string field theory solutions with matter operators from KBc algebra

Abstract The KBc algebra is a subalgebra that has been used to construct classical solutions in Witten’s open string field theory, such as the tachyon vacuum solution. The main purpose of this paper is to give various operator sets that satisfy the KBc algebra. In addition, since those sets can contain matter operators arbitrarily, we can reproduce the solution of Kiermaier, Okawa, and Soler, and that of Erler and Maccaferri. Starting with a single D-brane solution on the tachyon vacuum, we replace the original KBc in it with an appropriate set to generate each of the above solutions. Thus, it is expected that the KBc algebra, combined with the single D-brane solution, leads to a more unified description of classical solutions.

Large N phenomena and quantization of the Loday-Quillen-Tsygan theorem

We offer a new approach to large N limits using the Batalin-Vilkovisky formalism, both commutative and noncommutative, and we exhibit how the Loday-Quillen-Tsygan Theorem admits BV quantizations in that setting. Matrix integrals offer a key example: we demonstrate how this formalism leads to a recurrence relation that in principle allows us to compute all multi-trace correlation functions. We also explain how the Harer-Zagier relations may be expressed in terms of this noncommutative geometry derived from the BV formalism.As another application, we consider the problem of quantization in the large N limit and demonstrate how the Loday-Quillen-Tsygan Theorem leads us to a solution in terms of noncommutative geometry. These constructions are relevant to open topological field theories and string field theory, providing a mechanism that relates moduli of categories of branes to moduli of brane gauge theories.

Fate of the false vacuum in string-inspired nonlocal field theory

In this article, we study Coleman bounce in weakly nonlocal theories which are motivated from string field theory. The kinetic term is extended via an infinite series of high-order derivatives, which comes into play at an energy scale M, without introducing any new states or ghosts in the mass spectrum. We calculate the bubble nucleation in thin-wall approximation, treating the system in semi-classical manner. We find that the effect of nonlocal scale M in the theory is to suppress the vacuum tunneling rate from false to true vacuum compared to the standard local bouncing scenario. Likewise, we show that as we move further away from the bubble wall, the effects of nonlocality gets reduced and this suppression is significant only around the wall of the nucleated bubble. From our investigations, we conclude that the main effect is due to the fact that the nonlocality smears the solution of the local bubble profile. However, the energy of the bubble wall remains unaffected by the microscopic nonlocal behavior of the theory in the thin-wall approximation. We also discuss the cases for Lee-Wick theories and applications of our result to cosmology.

Missed opportunities of overcoming deadlocks

In this talk, I would like to speak about two projects that Igor Volovich and I discussed several years ago and which were never completed. The first one concerns string field theory in term of string generalization of vierbein and the second is about possible relations between matrix models and knots. I also discuss our recent projects connected with information paradox.

The gauge structure of double field theory follows from Yang-Mills theory

We show that to cubic order double field theory is encoded in Yang-Mills theory. To this end we use algebraic structures from string field theory as follows: The ${L}_{\ensuremath{\infty}}$-algebra of Yang-Mills theory is the tensor product $\mathcal{K}\ensuremath{\bigotimes}\mathfrak{g}$ of the Lie algebra $\mathfrak{g}$ of the gauge group and a ``kinematic algebra'' $\mathcal{K}$ that is a ${C}_{\ensuremath{\infty}}$-algebra. This structure induces a cubic truncation of an ${L}_{\ensuremath{\infty}}$-algebra on the subspace of level-matched states of the tensor product $\mathcal{K}\ensuremath{\bigotimes}\overline{\mathcal{K}}$ of two copies of the kinematic algebra. This ${L}_{\ensuremath{\infty}}$-algebra encodes double field theory. More precisely, this construction relies on a particular form of the Yang-Mills ${L}_{\ensuremath{\infty}}$-algebra following from string field theory or from the quantization of a suitable worldline theory.

BRST ghost-vertex operator in Witten's cubic open string field theory on multiple Dp-branes

The Becchi–Rouet–Stora–Tyutin (BRST) ghost field is a key element in constructing Witten's cubic open string field theory. However, to date, the ghost sector of the string field theory has not received a great deal of attention. In this study, we address the BRST ghost on multiple Dp-branes, which carries non-Abelian indices and couples to a non-Abelian gauge field. We found that the massless components of the BRST ghost field can play the role of the Faddeev–Popov ghost in the non-Abelian gauge field, such that the string field theory maintains the local non-Abelian gauge invariance.

Normalization of ZZ instanton amplitudes in minimal string theory

We use insights from string field theory to analyze and cure the divergences in the cylinder diagram in minimal string theory with both boundaries lying on a ZZ brane. We focus on theories with worldsheet matter consisting of the (2, p) minimal model plus Liouville theory, with total central charge 26, together with the usual bc-ghosts. The string field theory procedure gives a finite, purely imaginary normalization constant for non-perturbative effects in minimal string theory, or doubly non-perturbative effects in JT gravity. We find precise agreement with the prediction from the dual double-scaled one-matrix integral. We also make a few remarks about the extension of this result to the more general (p′, p) minimal string.

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.

Witten’s cubic open string field theory on multiple Dp-branes

We study Witten's cubic open string field theory on multiple $Dp$-branes. On multiple $Dp$-branes the string fields carry $U(N)$ group indices. Mapping the string world-sheet onto the upper half complex plane and evaluating the Polyakov string path integral of Witten's cubic open string, we obtain a Fock space representation of one, two and three-string vertex operators. In the low energy region, the system is described by massless gauge fields and massless scalar fields, carrying $U(N)$ group indices. The two-string vertex induces mass terms for the gauge fields and the scalar fields. The cubic interaction reduces correctly to the cubic term of the non-Abelian gauge fields, cubic interaction terms of the gauge fields, and the scalar fields on $(p+1)$ dimensional space. Thus, Witten's string field theory may be a useful tool to study the quantum dynamics of open strings on multiple $Dp$-branes.

Connections between reflected entropies and hyperbolic string vertices

In this paper, we establish connections between the reflected entropies of multipartite mixed states in CFT2 and hyperbolic string vertices of closed string field theory (CSFT). We show that the reflected surfaces, which are bulk duals of the reflected entropies, share the same Riemann surfaces with the hyperbolic string vertices. This observation enables us to build quantitative relations between the reflected entropies and hyperbolic string vertices. We illustrate the connections with several examples. Consequently, we propose that spacetime structure could be directly generated from the hyperbolic string vertices. The advantage of the hyperbolic string vertices approach is that we have a dynamical equation, the Batalin-Vilkoviski master equation, to control the generating process.

A toy model for background independent string field theory

We study gauge theories of background fields associated to BRST quantized spinning particle models and identify background-independent algebraic structures which allow to systematically reduce the spectrum of fields and subject some of them to dynamical equations of motion. More specifically, we construct a manifestly background-independent extension of the model based on N = 2 spinning particle. The resulting system describes an on-shell spin-1 field coupled to off-shell background fields including metric and dilaton. Tensoring with a given Lie algebra results in a non-abelian extension of the model.

The Riemann hypothesis and tachyonic off-shell string scattering amplitudes

The study of the mathbf{4}-tachyon off-shell string scattering amplitude A_4 (s, t, u) , based on Witten’s open string field theory, reveals the existence of poles in the s-channel and associated to a continuum of complex “spins” J. The latter J belong to the Regge trajectories in the t, u channels which are defined by - J (t) = - 1 - { 1over 2 } t = beta (t)= { 1over 2 } + i lambda ; - J (u) = - 1 - { 1over 2 } u = gamma (u) = { 1over 2 } - i lambda , with lambda = real. These values of beta ( t ), gamma (u) given by { 1over 2 } pm i lambda , respectively, coincide precisely with the location of the critical line of nontrivial Riemann zeta zeros zeta (z_n = { 1over 2 } pm i lambda _n) = 0. It is argued that despite assigning angular momentum (spin) values J to the off-shell mass values of the external off-shell tachyons along their Regge trajectories is not physically meaningful, their net zero-spin value J ( k_1 ) + J (k_2) = J ( k_3 ) + J ( k_4 ) = 0 is physically meaningful because the on-shell tachyon exchanged in the s-channel has a physically well defined zero-spin. We proceed to prove that if there were nontrivial zeta zeros (violating the Riemann Hypothesis) outside the critical line Real~ z = 1/2 (but inside the critical strip) these putative zeros don't correspond to any poles of the mathbf{4}-tachyon off-shell string scattering amplitude A_4 (s, t, u) . We finalize with some concluding remarks on the zeros of sinh(z) given by z = 0 + i 2 pi n, continuous spins, non-commutative geometry and other relevant topics.

Multipartitioning topological phases by vertex states and quantum entanglement

We discuss multipartitions of the gapped ground states of (2+1)-dimensional topological liquids into three (or more) spatial regions that are adjacent to each other and meet at points. By considering the reduced density matrix obtained by tracing over a subset of the regions, we compute various correlation measures, such as entanglement negativity, reflected entropy, and associated spectra. We utilize the bulk-boundary correspondence to show that such multipartitions can be achieved by using what we call vertex states in (1+1)-dimensional conformal field theory -- these are a type of state used to define an interaction vertex in string field theory and can be thought of as a proper generalization of conformal boundary states. This approach allows an explicit construction of the reduced density matrix near the entangling boundaries. We find the fingerprints of topological liquid in these quantities, such as (universal pieces in) the scaling of the entanglement negativity, and a non-trivial distribution of the spectrum of the partially transposed density matrix. For reflected entropy, we test the recent claim that states the difference between reflected entropy and mutual information is given, once short-range correlations are properly removed, by $(c/3)\ln 2$ where $c$ is the central charge of the topological liquid that measures ungappable edge degrees of freedom. As specific examples, we consider topological chiral $p$-wave superconductors and Chern insulators. We also study a specific lattice fermion model realizing Chern insulator phases and calculate the correlation measures numerically, both in its gapped phases and at critical points separating them.

Dimensional reduction of higher derivative heterotic supergravity

Higher derivative couplings of hypermultiplets to 6D, N = (1, 0) supergravity are obtained from dimensional reduction of 10D heterotic supergravity that includes order α′ higher derivative corrections. Reduction on T4 is followed by a consistent truncation. In the resulting action the hyperscalar fields parametrize the coset SO(4, 4)/(SO(4) × SO(4)). While the SO(4, 4) symmetry is ensured by Sen’s construction based on string field theory, its emergence at the field theory level is a nontrivial phenomenon. A number of field redefinitions in the hypermultiplet sector are required to remove several terms that break the SO(4) × SO(4) down to its SO(4) diagonal subgroup in the action and the supersymmetry transformation rules. Working with the Lorentz Chern-Simons term modified 3-form field strength, where the spin connection has the 3-form field strength as torsion, is shown to simplify considerably the dimensional reduction.

Erratum to: Proof of new S-matrix formula from classical solutions in open string field theory: Or, deriving on-shell open string field amplitudes without using Feynman rules, Part II

Erratum to: Proof of new S-matrix formula from classical solutions in open string field theory: Or, deriving on-shell open string field amplitudes without using Feynman rules, Part II