Bosonic String Research Articles

The B-field soft theorem and its unification with the graviton and dilaton

In theories of Einstein gravity coupled with a dilaton and a two-form, a soft theorem for the two-form, known as the Kalb-Ramond B-field, has so far been missing. In this work we fill the gap, and in turn formulate a unified soft theorem valid for gravitons, dilatons and B-fields in any tree-level scattering amplitude involving the three massless states. The new soft theorem is fixed by means of on-shell gauge invariance and enters at the subleading order of the graviton’s soft theorem. In contrast to the subsubleading soft behavior of gravitons and dilatons, we show that the soft behavior of B-fields at this order cannot be fully fixed by gauge invariance. Nevertheless, we show that it is possible to establish a gauge invariant decomposition of the amplitudes to any order in the soft expansion. We check explicitly the new soft theorem in the bosonic string and in Type II superstring theories, and furthermore demonstrate that, at the next order in the soft expansion, totally gauge invariant terms appear in both string theories which cannot be factorized into a soft theorem.

O(d+1, d+1) enhanced double field theory

Double field theory yields a formulation of the low-energy effective action of bosonic string theory and half-maximal supergravities that is covariant under the T-duality group O(d, d) emerging on a torus Td. Upon reduction to three spacetime dimensions and dualisation of vector fields into scalars, the symmetry group is enhanced to O(d+1, d+1). We construct an enhanced double field theory with internal coordinates in the adjoint representation of O(d + 1, d + 1). Its section constraints admit two inequivalent solutions, encoding in particular the embedding of D = 6 chiral and non-chiral theories, respectively. As an application we define consistent generalized Scherk-Schwarz reductions using a novel notion of generalized parallelization. This allows us to prove the consistency of the truncations of D = 6, mathcal{N}=left(1,1right) and D = 6, mathcal{N}=left(2,0right) supergravity on {mathrm{AdS}}_3times {mathbb{S}}^3 .

Double Field Theory description of heterotic gauge symmetry enhancing-breaking

A Double Field Theory (DFT) description of gauge symmetry enhancing-breaking in the heterotic string is presented. The construction, based on previous results for the bosonic string, relies on the extension of the tangent frame of DFT. The fluxes of a Scherk-Schwarz like generalized toroidal compactification are moduli dependent and become identified with the structure constants of the enhanced group at fixed “self-dual” points in moduli space. Slight displacements from such points provide the breaking of the symmetry, gauge bosons acquiring masses proportional to fluxes. The inclusion of fermions is also discussed.

Loss of locality in gravitational correlators with a large number of insertions

We review lessons from the AdS/CFT correspondence that indicate that the emergence of locality in quantum gravity is contingent upon considering observables with a small number of insertions. Correlation functions, where the number of insertions scales with a power of the central charge of the CFT, are sensitive to nonlocal effects in the bulk theory, which arise from a combination of the effects of the bulk Gauss law and a breakdown of perturbation theory. To examine whether a similar effect occurs in flat space, we consider the scattering of massless particles in the bosonic string and the superstring in the limit, where the number of external particles, n, becomes very large. We use estimates of the volume of the Weil-Petersson moduli space of punctured Riemann surfaces to argue that string amplitudes grow factorially in this limit. We verify this factorial behavior through an extensive numerical analysis of string amplitudes at large n. Our numerical calculations rely on the observation that, in the large n limit, the string scattering amplitude localizes on the Gross-Mende saddle points, even though individual particle energies are small. This factorial growth implies the breakdown of string perturbation theory for $n\ensuremath{\sim}{(\frac{{M}_{\mathrm{pl}}}{E})}^{d\ensuremath{-}2}$ in $d$ dimensions, where $E$ is the typical individual particle energy. We explore the implications of this breakdown for the black hole information paradox. We show that the loss of locality suggested by this breakdown is precisely sufficient to resolve the cloning and strong subadditivity paradoxes.

Fricke Lie algebras and the genus zero property in Moonshine

We give a new, simpler proof that the canonical actions of finite groups on Fricke-type Monstrous Lie algebras yield genus zero functions in generalized Monstrous Moonshine, using a Borcherds–Kac–Moody Lie algebra decomposition due to Jurisich. We describe a compatibility condition, arising from the no-ghost theorem in bosonic string theory, that yields the genus zero property. We give evidence for and against the conjecture that such a compatibility for symmetries of the Monster Lie algebra gives a characterization of the Monster group.

Mathcal{N} = 2 S-duality revisited

Using the chiral algebra bootstrap, we revisit the simplest Argyres-Douglas (AD) generalization of Argyres-Seiberg S-duality. We argue that the exotic AD superconformal field theory (SCFT), {mathcal{T}}_{3,frac{3}{2}} , emerging in this duality splits into a free piece and an interacting piece, {mathcal{T}}_X , even though this factorization seems invisible in the Seiberg-Witten (SW) curve derived from the corresponding M5-brane construction. Without a Lagrangian, an associated topological field theory, a BPS spectrum, or even an SW curve, we nonetheless obtain exact information about {mathcal{T}}_X by bootstrapping its chiral algebra, {}_{mathcal{X}}left({mathcal{T}}_Xright) , and finding the corresponding vacuum character in terms of Affine Kac-Moody characters. By a standard 4D/2D correspondence, this result gives us the Schur index for {mathcal{T}}_X and, by studying this quantity in the limit of small S1, we make contact with a proposed S1 reduction. Along the way, we discuss various properties of {mathcal{T}}_X : as an mathcal{N} = 1 theory, it has flavor symmetry SU(3) × SU(2) × U(1), the central charge of {}_{mathcal{X}}left({mathcal{T}}_Xright) matches the central charge of the bc ghosts in bosonic string theory, and its global SU(2) symmetry has a Witten anomaly. This anomaly does not prevent us from building conformal manifolds out of arbitrary numbers of {mathcal{T}}_X theories (giving us a surprisingly close AD relative of Gaiotto’s TN theories), but it does lead to some open questions in the context of the chiral algebra/4D mathcal{N} =2SCFT correspondence.

Singular gauge transformation and the Erler–Maccaferri solution in bosonic open string field theory

We study candidates of the multiple-brane solutions of bosonic open string field theory. They are constructed by performing a singular gauge transformation $n$ times for the Erler-Maccaferri solution. We check the EOM in the strong sense, and find that it is satisfied only when we perform the gauge transformation once. We calculate the energy for that case and obtain a support that the solution is a multiple-brane solution. We also check the tachyon profile for a specific solution which we interpret as describing a D24-brane placed on a D25-brane.

Solving Lauricella string scattering amplitudes through recurrence relations

We show that there exist infinite number of recurrence relations valid for all energies among the open bosonic string scattering amplitudes (SSA) of three tachyons and one arbitrary string state, or the Lauricella SSA. Moreover, these infinite number of recurrence relations can be used to solve all the Lauricella SSA and express them in terms of one single four tachyon amplitude. These results extend the solvability of SSA at the high energy, fixed angle scattering limit and those at the Regge scattering limit discovered previously to all kinematic regimes.

Gauge symmetry enhancing-breaking from a Double Field Theory perspective

Gauge symmetry enhancing, at specific points of the compactification space, is a distinguished feature of string theory. In this work we discuss the breaking of such symmetries with tools provided by Double Field Theory (DFT). As a main guiding example we discuss the bosonic string compactified on a circle where, at the self-dual radio the generic U(1) × U(1) gauge symmetry becomes enhanced to SU(2) × SU(2). We show that the enhancing-breaking of the gauge symmetry can be understood through a dependence of gauge structure constants (fluxes in DFT) on moduli. This dependence, in DFT description, is encoded in the generalized tangent frame of the double space. The explicit T-duality invariant formulation provided by DFT proves to be a helpful ingredient. The link with string theory results is discussed and generalizations to generic tori compactifications are addressed.

Stringy AdS3 from the worldsheet

We investigate the behaviour of the bosonic string on AdS3 with H-flux at stringy scales, looking in particular for a ‘tensionless’ limit in which there are massless higher spin gauge fields. We do this by revisiting the physical spectrum of the mathfrak{s}mathfrak{l}{left(2, mathbb{R}right)}_k WZW model and considering the limit in which k becomes small. At k = 3 we find that there is an infinite stringy tower of massless higher spin fields which are part of a continuum of light states. This can be viewed as a novel tensionless limit, which appears to be distinct from that inferred from the symmetric orbifold description of superstring AdS3 vacua.

The bosonic string on string-size tori from double field theory

We construct the effective action for toroidal compactifications of bosonic string theory from generalized Scherk-Schwarz reductions of double field theory. The enhanced gauge symmetry arising at special points in moduli space is incorporated into this framework by promoting the O(k, k) duality group of k-tori compactifications to O(n, n), n being the dimension of the enhanced gauge group, which allows to account for the full massless sector of the theory. We show that the effective action reproduces the right masses of scalar and vector fields when moving sligthly away from the points of maximal symmetry enhancement. The neighborhood of the enhancement points in moduli space can be neatly explored by spontaneous symmetry breaking. We generically discuss toroidal com-pactifications of arbitrary dimensions and maximally enhanced gauge groups, and then inspect more closely the example of T2 at the SU(3)L × SU(3)R point, which is the simplest setup containing all the non-trivialities of the generic case. We show that the entire moduli space can be described in a unified way by considering compactifications on higher dimensional tori.

Stability of the nonperturbative bosonic string vacuum

Quantization of the bosonic string around the classical, perturbative vacuum is not consistent for spacetime dimensions 2<d<26. Recently we have showed that at large d there is another so-called mean-field vacuum. Here we extend this mean-field calculation to finite d and show that the corresponding mean-field vacuum is stable under quadratic fluctuations for 2<d<26. We point out the analogy with the two-dimensional O(N)-symmetric sigma-model, where the 1/N-vacuum is very close to the real vacuum state even for finite N, in contrast to the perturbative vacuum.

Weyl invariance for generalized supergravity backgrounds from the doubled formalism

It has recently been shown that a set of the generalized type IIB supergravity equations follows from the requirement of kappa symmetry of the type IIB Green-Schwarz superstring theory defined on an arbitrary background. In this paper, we show that the whole bosonic part of the generalized type II supergravity equations can be reproduced from the T-duality covariant equations of motion of the double field theory by choosing a non-standard solution of the strong constraint. Then, by using the doubled formalism, we show the Weyl invariance of the bosonic string sigma model on a generalized gravity background. According to the dual-coordinate dependence of the dilaton, the Fradkin-Tseytlin term nicely removes the Weyl anomaly. This result seems likely to support that string theories can be consistently defined on arbitrary generalized supergravity backgrounds.

Strings in Singular Space-Times and Their Universal Gauge Theory

We study the propagation of bosonic strings in singular target space-times. For describing this, we assume this target space to be the quotient of a smooth manifold $M$ by a singular foliation ${\cal F}$ on it. Using the technical tool of a gauge theory, we propose a smooth functional for this scenario, such that the propagation is assured to lie in the singular target on-shell, i.e. only after taking into account the gauge invariant content of the theory. One of the main new aspects of our approach is that we do not limit ${\cal F}$ to be generated by a group action. We will show that, whenever it exists, the above gauging is effectuated by a single geometrical and universal gauge theory, whose target space is the generalized tangent bundle $TM\oplus T^*M$.

Shining light on polarizable dark particles

We investigate the possibilities of searching for a self-conjugate polarizable particle in the self-interactions of light. We first observe that polarizability can arise either from the exchange of mediator states or as a consequence of the inner structure of the particle. To exemplify this second possibility we calculate the polarizability of a neutral bosonic open string, and find it is described only by dimension-8 operators. Focussing on the spin-0 case, we calculate the light-by-light scattering amplitudes induced by the dimension-6 and 8 polarizability operators. Performing a simulation of exclusive diphoton production with proton tagging at the LHC, we find that the imprint of the polarizable dark particle can be potentially detected at 5σ significance for mass and cutoff reaching values above the TeV scale, for sqrt{s}=13 TeV and 300 fb−1 of integrated luminosity. If the polarizable dark particle is stable, it can be a dark matter candidate, in which case we argue this exclusive diphoton search may complement the existing LHC searches for polarizable dark matter.

The Odd story of \u03b1\u2032-corrections

The α′-deformed frame-like Double Field Theory (DFT) is a T-duality and gauge invariant extension of DFT in which generalized Green-Schwarz transformations provide a gauge principle that fixes the higher-derivative corrections. It includes all the first order α′-corrections of the bosonic and heterotic string low energy effective actions and of the Hohm-Siegel-Zwiebach α′-geometry. Here we gauge this theory and parameterize it in terms of a frame, a two-form, a dilaton, gauge vectors and scalar fields. This leads to a unified framework that extends the previous construction by including all duality constrained interactions in generic (gauged/super)gravity effective field theories in arbitrary number of dimensions, to first order in α′.

Background independent double field theory at order α′ : Metric versus framelike geometry

The higher derivative corrections in double field theory are revisited to first order in $\alpha'$. In first order perturbation theory around flat space, the gauge algebra is $\alpha'$ corrected, governed by two parameters $a, b$. One parameter choice corresponds to bosonic string theory, another to heterotic string theory. These results are generalized to second order in perturbation theory by a Noether procedure. Using consistency conditions derived from the Jacobi identity, it is shown that for general $a, b$ there is no generalized metric formulation. A manifestly background independent formulation is instead given by a frame formalism, with $\alpha'$-deformed frame transformations, as proposed by Marques and Nunez. Their construction is slightly generalized to an $\alpha'$-deformed $GL(D)\times GL(D)$ frame formalism. The perturbation theory around flat space is matched to second order with the results obtained by the Noether procedure. We also obtain a formulation based on the `non-symmetric' metric ${\cal E}$, the sum of metric and $b$-field. The transformations of ${\cal E}$ under $O(D,D)$ receive non-trivial $\alpha'$ corrections, unless $a=-b$, in which case there is a generalized metric formulation, in agreement with previous results in the literature.

Background Independence and Duality Invariance in String Theory.

Closed string theory exhibits an O(D,D) duality symmetry on tori, which in double field theory is manifest before compactification. I prove that to first order in α^{'} there is no manifestly background independent and duality invariant formulation of bosonic string theory in terms of a metric, b field, and dilaton. To this end I use O(D,D) invariant second order perturbation theory around flat space to show that the unique background independent candidate expression for the gauge algebra at order α^{'} is inconsistent with the Jacobi identity. A background independent formulation exists instead for frame variables subject to α^{'}-deformed frame transformations (generalized Green-Schwarz transformations). Potential applications for curved backgrounds, as in cosmology, are discussed.

Deformation of the cubic open string field theory

We study a consistent deformation of the cubic open bosonic string theory in such a way that the non-planar world sheet diagrams of the perturbative string theory are mapped onto their equivalent planar diagrams of the light-cone string field theory with some length parameters fixed. An explicit evaluation of the cubic string vertex in the zero-slope limit yields the correct relationship between the string coupling constant and the Yang–Mills coupling constant. The deformed cubic open string field theory is shown to produce the non-Abelian Yang–Mills action in the zero-slope limit if it is defined on multiple D-branes. Applying the consistent deformation systematically to multi-string world sheet diagrams, we may be able to calculate scattering amplitudes with an arbitrary number of external open strings.

Probing the string winding sector

We probe a slice of the massive winding sector of bosonic string theory from toroidal compactifications of Double Field Theory (DFT). This string subsector corresponds to states containing one left and one right moving oscillators. We perform a generalized Kaluza Klein compactification of DFT on generic 2n-dimensional toroidal constant backgrounds and show that, up to third order in fluctuations, the theory coincides with the corresponding effective theory of the bosonic string compactified on n-dimensional toroidal constant backgrounds, obtained from three-point amplitudes. The comparison between both theories is facilitated by noticing that generalized diffeomorphisms in DFT allow to fix generalized harmonic gauge conditions that help in identifying the physical degrees of freedom. These conditions manifest as conformal anomaly cancellation requirements on the string theory side. The explicit expression for the gauge invariant effective action containing the physical massless sector (gravity+antisymmetric+gauge+ scalar fields) coupled to towers of generalized Kaluza Klein massive states (corresponding to compact momentum and winding modes) is found. The action acquires a very compact form when written in terms of fields carrying O(n, n) indices, and is explicitly T-duality invariant. The global algebra associated to the generalized Kaluza Klein compactification is discussed.