String Field Theory Research Articles

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 ≥ 0. These volumes can be shown to satisfy a recursion relation through a modification of Mirzakhani’s recursion as long as L ≤ 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.

Bulk-induced D-brane deformations and the string coupling constant

We consider computing the on-shell disk action of open-closed string field theory as a gauge-invariant way of capturing the shift in D-brane tension that is induced by a deformation of the bulk CFT. We study the effect of bulk matter deformations (both marginal and relevant) on a wide range of boundary conditions in a number of CFTs up to subleading (two-loop) order in perturbation theory. In all analyzed examples, we find that the shift in the g-function of the matter boundary state is always accompanied by a boundary-independent shift in the string coupling constant, whose leading behaviour is universally proportional to the sphere two-point function of the deforming bulk operator.

Algebras and Hilbert spaces from gravitational path integrals. Understanding Ryu-Takayanagi/HRT as entropy without AdS/CFT

Recent works by Chandrasekaran, Penington, and Witten have shown in various special contexts that the quantum-corrected Ryu-Takayanagi (RT) entropy (or its covariant Hubeny-Rangamani-Takayanagi (HRT) generalization) can be understood as computing an entropy on an algebra of bulk observables. These arguments do not rely on the existence of a local holographic dual field theory. We show that analogous-but-stronger results hold in any UV-completion of asymptotically anti-de Sitter quantum gravity with a Euclidean path integral satisfying a simple and (largely) familiar set of axioms. We consider a quantum context in which a standard Lorentz-signature classical bulk limit would have Cauchy slices with asymptotic boundaries BL ⊔ BR where both BL and BR are compact manifolds without boundary. Our main result is then that (the UV-completion of) the quantum gravity path integral defines type I von Neumann algebras ALBL\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\mathcal{A}}_L^{B_L} $$\\end{document}, ARBR\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\mathcal{A}}_R^{B_R} $$\\end{document} of observables acting respectively at BL, BR such that ALBL\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\mathcal{A}}_L^{B_L} $$\\end{document}, ARBR\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\mathcal{A}}_R^{B_R} $$\\end{document} are commutants. The path integral also defines entropies on ALBL\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\mathcal{A}}_L^{B_L} $$\\end{document}, ARBR\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\mathcal{A}}_R^{B_R} $$\\end{document}. Positivity of the Hilbert space inner product then turns out to require the entropy of any projection operator to be quantized in the form ln N for some N ∈ ℤ+ (unless it is infinite). As a result, our entropies can be written in terms of standard density matrices and standard Hilbert space traces. Furthermore, in appropriate semiclassical limits our entropies are computed by the RT-formula with quantum corrections. Our work thus provides a Hilbert space interpretation of the Ryu-Takayanagi entropy. Since our axioms do not severely constrain UV bulk structures, it is plausible that they hold equally well for successful formulations of string field theory, spin-foam models, or any other approach to constructing a UV-complete theory of gravity.

Open String Renormalization Group Flow as a Field Theory

AbstractThis article shows that the integral flow‐lines of the RG‐flow of open string theory can be interpreted as the solitons of a Hořova–Lifshitz sigma‐model of open membranes. The authors argue that the effective background description of this model implies the g‐theorem of open string theory. Its close connection to boundary string field theory is described. Additionally, the study endows the Hilbert space of the open membrane with a graded non‐commutative, associative, cyclic algebra and construct an open membrane field theory, whose action measures the energy difference between different backgrounds in open string field theory. The authors use an identity‐based membrane field to proof Sen's conjecture. Finally, the ideas are applied to the topological string and it is shown that the membrane action is quantized in equivariant K‐theory of the moduli space of framed instantons.

Revisiting elastic string models of forward interest rates

Twenty five years ago, several authors proposed to describe the forward interest rate curve (FRC) as an elastic string along which idiosyncratic shocks propagate, accounting for the peculiar structure of the return correlation across different maturities. In this paper, we revisit the specific ‘stiff’ elastic string field theory of Baaquie and Bouchaud [Stiff field theory of interest rates and psychological future time. Wilmott Mag., 2004, 2–6] in a way that makes its micro-foundation more transparent. Our model can be interpreted as capturing the effect of market forces that set the rates of nearby tenors in a self-referential fashion. The model is parsimonious and accurately reproduces the whole correlation structure of the FRC over the time period 1994–2023, with an error around 1% and with only one adjustable parameter, the value of which being very stable across the last three decades. The dependence of correlation on time resolution (also called the Epps effect) is also faithfully reproduced within the model and leads to a cross-tenor information propagation time on the order of 30 minutes. Finally, we confirm that the perceived time in interest rate markets is a strongly sub-linear function of real time, as surmised by Baaquie and Bouchaud [Stiff field theory of interest rates and psychological future time. Wilmott Mag., 2004, 2–6]. In fact, our results are fully compatible with hyperbolic discounting, in line with the recent behavioral Finance literature Farmer and Geanakoplos [Hyperbolic Discounting is Rational: Valuing the Far Future with Uncertain Discount Rates, Cowles Foundation Discussion Papers, 2009 (Cowles Foundation for Research in Economics, Yale University)].

Normalization of ZZ instanton amplitudes in type 0B minimal superstring theory

Abstract We study ZZ instanton corrections in the (2, 4k) $$ \mathcal{N} $$ N = 1 minimal superstring theory with the type 0B GSO projection, which becomes the type 0B $$ \mathcal{N} $$ N = 1 super-JT gravity in the k → ∞ limit. Each member of the (2, 4k) family of theories has two phases distinguished by the sign of the Liouville bulk cosmological constant. The worldsheet method for computing the one-loop normalization constant multiplying the instanton corrections gives an ill-defined answer in both phases. We fix these divergences using insights from string field theory and find finite, unambiguous results. Each member of the (2, 4k) family of theories is dual to a double-scaled one-matrix integral, where the double-scaling limit can be obtained starting either from a unitary matrix integral with a leading one-cut saddle point, or from a hermitian matrix integral with a leading two-cut saddle point. The matrix integral exhibits a gap-closing transition, which is the same as the double-scaled Gross-Witten-Wadia transition when k = 1. We also compute instanton corrections in the double-scaled matrix integral for all k and in both phases, and find perfect agreement with the string theory results.

Noether’s theorem and Ward-Takahashi identities from homotopy algebras

We derive the new identity in homotopy algebras which directly corresponds to the Schwinger-Dyson equations in quantum field theory. As an application, we derive the Ward-Takahashi identities. We demonstrate that the Ward-Takahashi identities are reproduced in several examples. In general, our formula contains divergence. We mediate this problem by introducing stubs known in the context of string field theory. With the regularization, we can calculate the anomaly such as axial U(1) anomaly in vector-like U(1) gauge theory.

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.

Adding stubs to quantum string field theories

Generalizing recent work by Schnabl-Stettinger and Erbin-Fırat, we outline a universal algebraic procedure for ‘adding stubs’ to string field theories obeying the BV quantum master equation. We apply our results to classical and quantum closed string field theory as well as to open-closed string field theory. We also clarify several aspects of the integration-out process in the co-algebraic formulation of string field theory at the quantum level.

A two parameter family of lightcone-like hyperbolic string vertices

We introduce a two parameter family of string field theory vertices, which we refer to as hyperbolic Kaku vertices. It is defined in terms of hyperbolic metrics on the Riemann surface, but the geometry is allowed to depend on inputs of the states. The vertices are defined for both open and closed strings. In either case, the family contains the hyperbolic vertices. Then we show that the open string lightcone vertex is obtained as the flat limit of the hyperbolic Kaku vertices. The open string Kaku vertices, which interpolate between the Witten vertex and the open string lightcone vertex, is also obtained as a flat limit. We use the same limit on the case of closed strings to define the closed string Kaku vertices: a one parameter family of vertices that interpolates between the polyhedral vertices — which are covariant, but not cubic — and the closed string lightcone vertex — which is cubic, but not Lorentz covariant.

Quantum deformation of cubic string field theory

In this paper, we will analyze a quantum deformation of cubic string field theory. This will be done by first constructing a quantum deformation of string theory, in a covariant gauge, and then using the quantum deformed stringy theory to construct a quantum deformation of string field theory. This quantum-deformed string field will then be used to contract a quantum-deformed version of cubic string field theory. We will explicitly demonstrate that the axioms of cubic string field theory hold even after quantum deformation. Finally, we will analyze the effect of the quantum deformation of string field theory on the string vertices.

Strebel Differentials and String Field Theory

Abstract A closed string worldsheet of genus g with n punctures can be presented as a contact interaction in which n semi-infinite cylinders are glued together in a specific way via the Strebel differential on it, if $n\ge 1,\ 2g-2+n\gt 0$. We construct a string field theory of closed strings such that all the Feynman diagrams are represented by such contact interactions. In order to do so, we define off-shell amplitudes in the underlying string theory using the combinatorial Fenchel–Nielsen coordinates to describe the moduli space and derive a recursion relation satisfied by them. Utilizing the Fokker–Planck formalism, we construct a string field theory from which the recursion relation can be deduced through the Schwinger–Dyson equation. The Fokker–Planck Hamiltonian consists of kinetic terms and three-string interaction terms.

Cosmological implications of Kalb-Ramond-like particles

The Kalb-Ramond field is an antisymmetric, rank-two tensor field which most notably appears in the context of string theory, but has largely been unexplored in the context of cosmology. In this work, motivated by the Kalb-Ramond field in string theory, and antisymmetric tensor fields that emerge in effective field theories ranging from particle physics to condensed matter, we study the primordial production of interacting massive Kalb-Ramond-like-particles (KRLPs). KRLPs contain features of both dark photon and axion models, which can be appreciated via their duality properties. While the massless non-interacting KRLP is dual to a pseudoscalar, and the massive non-interacting KRLP is dual to a pseudovector, the interacting massive KRLP can be distinguished from its scalar and vector counterparts. We study early-universe production of KRLPs via the freeze-in mechanism, considering a ‘dark photon-like’ interaction, an ‘axion-like’ interaction, and a ‘Higgs portal’ interaction, as well as production via cosmological gravitational particle production. We find that as a dark matter candidate, KRLPs can be produced by all of the above mechanisms and account for the relic density of dark matter today for a wide range of masses. Finally, we comment on the potential to obtain both warm and cold dark matter subcomponents, and speculate on observational and experimental prospects.

A worldsheet description of flux compactifications

We demonstrate how recent developments in string field theory provide a framework to systematically study type II flux compactifications with non-trivial Ramond-Ramond profiles. We present an explicit example where physical observables can be computed order by order in a small parameter which can be effectively viewed as string coupling constant. We obtain the corresponding background solution of the string field equations of motions up to the second order in the expansion. Along the way, we show how the tadpole cancellations of the string field equations lead to the minimization of the F-term potential of the low energy supergravity description. String field action expanded around the obtained background solution furnishes a “worldsheet” description of the flux compactifications.

On democratic string field theories

We reexamine democratic open string field theories, namely, theories in which string fields are not constrained to a single picture number and picture changing is obtained as a gauge transformation. We describe several possibilities for regular free theories and attempt to construct the lowest order interaction term and identify the lowest order gauge transformation for some of these theories. We also discuss projections over string field spaces that might be needed for a consistent off-shell implementation of picture changing.

Anomalies in string-inspired nonlocal extensions of QED

We investigate anomalies in the class of nonlocal field theories that have been proposed as an ultraviolet completion of four-dimensional quantum field theory with generalizing the kinetic energy operators to an infinite series of higher derivatives inspired by the string field theory and ghost-free nonlocal approaches to quantum gravity. We explicitly calculate the vector and chiral anomalies in a string-inspired nonlocal extension of QED. We show that the vector anomaly vanishes as required by gauge invariance and the Ward identity. On the other hand, although the chiral anomaly vanishes to the leading order with massless fermions, it nonetheless does not vanish with the massive fermions and we calculate it to the leading order in the scale of nonlocality. We also calculate the nonlocal vector and axial currents explicitly and present an illustrative example by applying our results to the decay of π0→γγ. Published by the American Physical Society 2024

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.

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.

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.

A stringy effect on Hawking radiation

In string theories, interactions are exponentially suppressed for trans-Planckian space-like external momenta. We study a class of quantum field theories that exhibit this feature modeled after Witten’s bosonic open string field theory, and discover a Lorentz-invariant UV/IR relation that leads to the spacetime uncertainty principle proposed by Yoneya. Application to a dynamical black hole background suggests that Hawking radiation is turned off around the scrambling time.