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Igor Pesando

Publications and source records attributed to Igor Pesando.

At least 19 recordsLinked to original sources
arXiv2026

All DDF/lightcone two-particle decay widths up to level $8$ in open bosonic string in critical dimension

We carry out an ``experimental analysis'' in which we explicitly compute all possible Abelian two-particle decay channels (excluding the tachyon) of open bosonic massive states up to level (8), amounting to approximately 2,000,000 cases. The aim is to develop intuition about which states are the most stable and to identify the dominant decay channels. Our results show that, for all levels considered, the ratio of decay widths between the slowest- and fastest-decaying states is of order one. In most cases, the dominant polarized decay channel accounts for at least $10\%$ of the total decay width, while the first five channels together contribute roughly 60%. Even when we sum about $10000$ polarized channels. Dominant polarized channels always involve at least one photon and all strings ultimately decay into a photon carrying energy at the string scale. The most stable states are made using the DDF/lightcone oscillators $A_{-1}$ and some $A_{-2}$ and are close relatives of the states on the leading Regge trajectory. Finally, we discuss how the computation on the lightcone differs from the equal-time computation due to ``surges'', i.e., decays into a tachyon and a higher-mass state, and we hypothesize that, in bosonic string theory, decays into tachyons constitute the dominant decay channels.

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arXiv2026

Classical strings and the double copy

The double copy is by now a well-established relationship between scattering amplitudes and classical solutions in gauge and gravity (field) theories, and is itself inspired by amplitude relations in string theory. In this paper, we generalise the classical double copy to the motion of strings, taking as a case study the motion of an open string in a background abelian gauge field. We argue that the double copy of this situation is a closed string moving in a spacetime background arising as the double copy of the gauge theory background. The gauge theory background we consider is that of a constant electric field, which has a critical value beyond which the open string motion is pathological. We find no counterpart of this behaviour in the double copy, and interpret this result. We then examine how the closed string nevertheless still knows about the single copy gauge theory. Our results pave the way for more systematic study of the double copy in a classical string context, thus going beyond the KLT relations for amplitudes in flat space.

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arXiv2025

Bosonic string massive scalar amplitudes and absence of "chaos''

We compute directly in covariant formalism various four point massive scalar amplitudes in bosonic string with scalars up to level 11. The most ``difficult'' amplitude we consider is four identical scalars at level 4, i.e. the first non trivial amplitude with four identical massive scalars. All other amplitudes have at least one tachyon. All computed amplitudes are perfectly regular and show no sign of erratic behavior. While this could be naively expected it is not completely trivial because of higher spins exchanged. We give a naive argument based on a very simple model of why this can reasonably be expected and we check on the explicit examples that the intuition derived from the model is sensible. Furthermore we discuss the complications due to null states (BRST exact states) in actually computing the covariant bosonic string spectrum and how these can be overcome by using a ``$\Pi$ gauge'' which makes manifest that the degeneration of any spin at any mass level is independent on the spacetime dimension as predicted by Curtright et al at the end of 90s.

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arXiv2024

DDF amplitudes are lightcone amplitudes and the naturalness of Mandelstam map

We show that on shell DDF amplitudes are on shell lightcone amplitudes and that Mandelstam maps emerge naturally with a precise normalization and are intrinsic to the DDF states. Off shell DDF and Mandelstam amplitudes \`a la Kaku-Kikkawa differ. Underway we give a very explicit formula for the conformal transformation of a generic vertex in the form of a compact generating function for free theories.

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arXiv2024

The Reggeon Vertex for DDF States

We provide a compact expression for the generating function of correlators involving an arbitrary number of bosonic open string DDF states. The explicit correlators for $M$ DDF states can then be obtained by differentiating this generating function with respect to the DDF polarization tensors. The generating function depends on single and double complex integrals centred around the punctures corresponding to the insertion points of the DDF vertices on the real axis in the upper half-plane. We have explicitly evaluated these integrals for an arbitrary number of DDF states. To check our results, we computed some massive scalars and spin-2 amplitudes for $M=3$ and $M=4$, verifying that these amplitudes have the form expected from Lorentz invariance. Moreover, for the first excited levels, we also show that the DDF amplitudes with generic polarizations can be reassembled into Lorentz-covariant amplitudes, with emergent covariant polarizations that match the expressions obtained by comparing the string states in both the DDF and covariant formalisms.

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arXiv2024

The bosonic string spectrum and the explicit states up to level $10$ from the lightcone and the chaotic behavior of certain string amplitudes

We compute the irreps and their multiplicities of bosonic string spectrum up to level 10 and we give explicitly the on shell lightcone states which make the irreps. For scalars and vectors we compute the multiplicity up to level 22 and 19 respectively. The first scalar at odd level appears at level 11. For the bosonic string in non critical dimensions we argue that at level $N$ there are always states transforming as tensors with $ s\ge N/2$ indices. Only in critical dimensions there are states with $s\le N/2$. Looking at the explicit coefficients of the combinations needed to make the irreps from the lightcone states we trace the origin of the chaotic behavior of certain cubic amplitudes considered in literature to the extremely precise and sensitive mixtures of states. For example the vectors at level $N=19$ are a linear combinations of states and when the coefficients are normalized to be integer some of them have more than 1200 figures.

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arXiv2024

Framed DDF operators and the general solution to Virasoro constraints

We define the framed DDF operators by introducing the concept of local frames in the usual formulation of DDF operators. In doing so it is possible to completely decouple the DDF operators from the associated tachyon and show that they are good zero-dimensional conformal operators. This allows for an explicit formulation of the general solution of the Virasoro constraints both on-shell and off-shell. We then make precise the realization of the intuitive idea that DDF operators can be used to embed light-cone states in the covariant formulation. This embedding is not unique, but depends on a coset. This coset is the little group of the embedding of the light-cone and is associated with a frame. The frame allows us to embed the $SO(D-2)$ light-cone physical polarizations into the $SO(1,D-1)$ covariant ones in the most general way. The solution to the Virasoro constraints is not in the gauge that is usually used. This happens since the states obtained from DDF operators are generically the sum of terms which are partially transverse due to the presence of a projector but not traceless and terms which are partially traceless but not transverse. To check the identification, we verify the matching of the expectation value of the second Casimir of the Poincar'e group for some light-cone states with the corresponding covariant states built using the framed DDFs.

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arXiv2022

On the breakdown of the perturbative interaction picture in Big Crunch/Big Bang or the true reason why perturbative string amplitudes on temporal orbifolds diverge

We discuss how the perturbative particle paradigm fails in certain background with space-like singularity but asymptotically flat which should admit a S-matrix. The Feynman approach relies on the interaction picture. This approach means that we can interpret interactions as exchanges of particles. Particles are the modes of the quadratic part of the Lagrangian. In certain backgrounds with space-like singularity the interaction Hamiltonian is well defined but the perturbative expansion of the evolution operator through the singularity and the perturbative $S$ matrix do not exist. On the other hand, relying on minisuperspace approximation we argue that the non perturbative evolution operator does exist. The complete breakdown of the perturbative expansion explains why the perturbative computations in the covariant formalism in string theory in temporal orbifold fail, at least at the tree level.

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arXiv2022

Light-Cone Quantization a of Scalar Field on Time-Dependent Backgrounds

We discuss what is light-cone quantization on a curved spacetime also without a null Killing vector. Then we consider as an example the light-cone quantization of a scalar field on a background with a Killing vector and the connection with the second quantization of the particle in the same background. It turns out that the proper way to define the light-cone quantization is to require that the constant light-cone time hypersurface is null or, equivalently, that the particle Hamiltonian is free of square roots. Moreover, in order to quantize the scalar theory it is necessary to use not the original scalar rather a scalar field density, i.e. the Schr\"odinger wave functional depends on a scalar density and not on the original field. Finally we recover this result as the second quantization of a particle on the same background, where it is necessary to add as input the fact that we are dealing with a scalar density.

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arXiv2020

On the Origin of Divergences in Time-Dependent Orbifolds

We consider time-dependent orbifolds in String Theory and we show that divergences are not associated with a gravitational backreaction since they appear in the open string sector too. They are related to the non existence of the underlying effective field theory as in several cases fourth and higher order contact terms do not exist. Since contact terms may arise from the exchange of string massive states, we investigate and show that some three points amplitudes with one massive state in the open string sector are divergent on the time-dependent orbifolds. To check that divergences are associated with the existence of a discrete zero eigenvalue of the Laplacian of the subspace with vanishing volume, we construct the Generalized Null Boost Orbifold where this phenomenon can be turned on and off.

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arXiv2019

2D Fermion on the Strip with Boundary Defects as a CFT with Excited Spin Fields

We consider a two-dimensional fermion on the strip in the presence of an arbitrary number of zero-dimensional boundary changing defects. We show that the theory is still conformal with time dependent stress-energy tensor and that the allowed defects can be understood as excited spin fields. Finally we compute correlation functions involving these excited spin fields without using bosonization.

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arXiv2018

The Classical Solution for the Bosonic String in the Presence of Three D-branes Rotated by Arbitrary SO(4) Elements

We consider the classical instantonic contribution to the open string configuration associated with three D-branes with relative rotation matrices in SO(4) which corresponds to the computation of the classical part of the correlator of three non Abelian twist fields. We write the classical solution as a sum of a product of two hypergeometric functions. Differently from all the previous cases with three D-branes, the solution is not holomorphic and suggests that the classical bosonic string knows when the configuration may be supersymmetric. We show how this configuration reduces to the standard Abelian twist field computation. From the phenomenological point of view, the Yukawa couplings between chiral matter at the intersection in this configuration are more suppressed with respect to the factorized case in the literature.

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arXiv2017

On the gauge chosen by the bosonic open string

String theory gives S matrix elements om which is not possible to read any gauge information. Using factorization we go off shell in the simplest and most naive way and we read which are the vertices suggested by string. To compare with the associated Effective Field Theory it is natural to use color ordered vertices. The alpha'=0 color ordered vertices suggested by string theory are more efficient than the usual ones since the three gluon color ordered vertex has three terms instead of six and the four gluon one has one term instead of three. They are written in the so called Gervais-Neveu gauge. The full Effective Field Theory is in a generalization of the Gervais-Neveu gauge with alpha') corrections. Moreover a field redefinition is required to be mapped to the field used by string theory. We also give an intuitive way of understanding why string choose this gauge in terms of the minimal number of couplings necessary to reproduce the non abelian amplitudes starting from color ordered ones.

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arXiv2015

Towards a fully stringy computation of Yukawa couplings on non factorized tori and non abelian twist correlators (I): the classical solution and action

We consider the simplest possible setting of non abelian twist fields which corresponds to $SU(2)$ monodromies. We first review the theory of hypergeometric function and of the solutions of the most general Fuchsian second order equation with three singularities. Then we solve the problem of writing the general solution with prescribed $U(2)$ monodromies. We use this result to compute the classical string solution corresponding to three $D2$ branes in $R^4$. Despite the fact the configuration is supersymmetric the classical string solution is not holomorphic. Using the equation of motion and not the KLT approach we give a very simple expression for the classical action of the string. We find that the classical action is not proportional to the area of the triangle determined by the branes intersection points since the solution is not holomorphic. Phenomenologically this means that the Yukawa couplings for these supersymmetric configurations on non factorized tori are suppressed with respect to the factorized case.

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arXiv2014

Canonical quantization of a string describing $N$ branes at angles

We study the canonical quantization of a bosonic string in presence of N twist fields. This generalizes the quantization of the twisted string in two ways: the in and out states are not necessarily twisted and the number of twist fields N can be bigger than 2. In order to quantize the theory we need to find the normal modes. Then we need to define a product between two modes which is conserved. Because of this we need to use the Klein-Gordon product and to separate the string coordinate into the classical and the quantum part. The quantum part has different boundary conditions than the original string coordinates but these boundary conditions are precisely those which make the operator describing the equation of motion self adjoint. The splitting of the string coordinates into a classical and quantum part allows the formulation of an improved overlap principle. Using this approach we then proceed in computing the generating function for the generic correlator with L untwisted operators and N (excited) twist fields for branes at angles. We recover as expected the results previously obtained using the path integral. This construction explains why these correlators

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arXiv2013

Light cone quantization and interactions of a new closed bosonic string inspired to D1 string

We quantize the bosonic part of the D1 string with closed boundary conditions on the light cone and we consider the U(1) worldsheet gauge field a dynamical variable. We compute also 3-Reggeon vertex by the overlapping technique. We find that the Fock space is the sum of sectors characterized by the momentum of the U(1) Wilson line and that these sectors do not interact among them. Each sector has exactly the same spectrum of the usual bosonic string when expressed in properly sector dependent rescaled variables. Rescaling is forced by factorization of the string amplitudes. We are also able to determine the relative string coupling constant of the different sectors. It follows a somewhat unexpected picture in which the effective action is always the same independently on the sector but string amplitudes are only the same when expressed in sector dependent rescaled variables.

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arXiv2013

Deformed N=2 theories, generalized recursion relations and S-duality

We study the non-perturbative properties of N=2 super conformal field theories in four dimensions using localization techniques. In particular we consider SU(2) gauge theories, deformed by a generic epsilon-background, with four fundamental flavors or with one adjoint hypermultiplet. In both cases we explicitly compute the first few instanton corrections to the partition function and the prepotential using Nekrasov's approach. These results allow to reconstruct exact expressions involving quasi-modular functions of the bare gauge coupling constant and to show that the prepotential terms satisfy a modular anomaly equation that takes the form of a recursion relation with an explicitly epsilon-dependent term. We then investigate the implications of this recursion relation on the modular properties of the effective theory and find that with a suitable redefinition of the prepotential and of the effective coupling it is possible, at least up to the third order in the deformation parameters, to cast the S-duality relations in the same form as they appear in the Seiberg-Witten solution of the undeformed theory.

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