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Francisco Rojas

Publications and source records attributed to Francisco Rojas.

15 recordsLinked to original sources
arXiv2026

Schwinger-Keldysh Cosmological Cutting Rules

In this work, we study the realisation of unitarity-based cutting rules for primordial cosmological correlators computed within the Schwinger-Keldysh path integral formalism. While cutting rules have been previously derived for wavefunction coefficients, here we examine them directly at the level of cosmological observables expressed diagrammatically. The resulting rules closely resemble those familiar from flat-space scattering amplitudes, but with an additional subtlety: in order to express the discontinuity of a correlator as the product of lower-order correlators, one must introduce a specific combinations of diagrams which do not appear in the computation of observables themselves. We explicitly verify these rules for several classes of correlators, both at tree level and with loop corrections, arising from theories involving different types of interactions.

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arXiv2025

Celestial closed strings at one-loop

In this paper we continue our investigation of superstring scattering amplitudes in the conformal basis. We focus on the case of four graviton scattering processes at 1-loop in \emph{closed} superstring theory. We write the expression for such a process in the celestial variables and confirm previous expectations. In particular, we find the adequate overall factorization of the $α'$ dependence which organizes the loop expansion of closed string celestial amplitudes. We also show that, at 1-loop, the field theory limit, when properly defined, commutes with the Mellin transform of the amplitudes for all values of the conformally invariant cross-ratio, something that had already been observed for gluon processes at 1-loop in open string theory and is to be compared with the tree-level computations. This indicates that many of the features satisfied for open string gluon amplitudes at tree and 1-loop levels are also universal properties of graviton celestial amplitudes in closed string theory. As a by-product, we also compute field theory graviton amplitudes at 1-loop in the conformal basis.

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arXiv2024

Celestial strings: field theory, conformally soft limits, and mapping the worldsheet onto the celestial sphere

We compute the celestial correlators corresponding to tree-level 5-gluon amplitudes in the type I superstring theory. Since celestial correlation functions are obtained by integrating over the full range of energies, there is no obvious analog of the $α' \to 0$ limit in this basis. This is manifestly shown by a factorization of the $α'$ dependence in the celestial string amplitudes. Consequently, the question arises as to how the field theory limit is recovered from string theory in the celestial basis. This problem has been addressed in the literature for the case of 4-gluon amplitudes at tree level, where the forward scattering limit of the stringy factor was identified as a limit in which celestial Yang-Mills 4-point function is recovered. Here, we extend the analysis to the case with five gluons, for which the string moduli space allows for more types of limits, thus allowing to investigate this aspect in more detail. Based on celestial data only, we study the regime in which one arrives at the correct celestial field theory limit. We also study other properties of the celestial string amplitudes, namely, the conformally soft theorem, effective field theory expansion in the conformal basis, and a map that arises in the regime of high-energy/large-scaling dimension that connects the punctured string worldsheet to the insertion of primary operators in the celestial CFT for the massless $n$-point string amplitude.

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arXiv2023

Celestial open strings at one-loop

We study celestial amplitudes in string theory at one-loop. Celestial amplitudes describe scattering processes of boost eigenstates and relate to amplitudes in the more standard basis of momentum eigenstates through a Mellin transform. They are thus sensitive to both the ultraviolet and the infrared, which raises the question of how to appropriately take the field theory limit of string amplitudes in the celestial basis. We address this problem in the context of four-dimensional genus-one scattering processes of gluons in open string theory which reach the two-dimensional celestial sphere at null infinity. We show that the Mellin transform commutes with the adequate limit in the worldsheet moduli space and reproduces the celestial one-loop field theory amplitude expressed in the worldline formalism. The dependence on $α'$ continues to be a simple overall factor in one-loop celestial amplitudes albeit with a power that is shifted by three units with respect to tree-level, thus making manifest that the dimensionless parameter $g_{10}^2/α'^3$ organizes the loop expansion in the celestial basis.

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arXiv2021

Celestial IR divergences in general most-subleading-color gluon and gravity amplitudes

Gluon amplitudes at most-subleading order in the $1/N$ expansion share a remarkable simplicity with graviton amplitudes: collinear divergences are completely absent in both and, as a consequence, their full IR behavior arises from soft gluon/graviton exchange among the external states. In this paper we study the effect of all-loop IR divergences of celestial most-subleading color gluon amplitudes and their similarities with the celestial gravity case. In particular, a simple celestial exponentiation formula for the dipole part can be written. We also analize how this exponentiation is modified by non-dipole contributions. Finally we also show that, in the Regge limit, the soft factor satisfies the Knizhnik-Zamolodchikov equation hinting at the possibility that, in this limit, an effective Wess-Zumino-Witten model would describe the dynamics of the infrared sector.

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arXiv2021

The structure of IR divergences in celestial gluon amplitudes

The all-loop resummation of SU$(N)$ gauge theory amplitudes is known to factorize into an IR-divergent (soft and collinear) factor and a finite (hard) piece. The divergent factor is universal, whereas the hard function is a process-dependent quantity. We prove that this factorization persists for the corresponding celestial amplitudes. Moreover, the soft/collinear factor becomes a scalar correlator of the product of renormalized Wilson lines defined in terms of celestial data. Their effect on the hard amplitude is a shift in the scaling dimensions by an infinite amount, proportional to the cusp anomalous dimension. This leads us to conclude that the celestial-IR-safe gluon amplitude corresponds to a expectation value of operators dressed with Wilson line primaries. These results hold for finite $N$. In the large $N$ limit, we show that the soft/collinear correlator can be described in terms of vertex operators in a Coulomb gas of colored scalar primaries with nearest neighbor interactions. In the particular cases of four and five gluons in planar $\mathcal{N}=4$ SYM theory, where the hard factor is known to exponentiate, we establish that the Mellin transform converges in the UV thanks to the fact that the cusp anomalous dimension is a positive quantity. In other words, the very existence of the full celestial amplitude is owed to the positivity of the cusp anomalous dimension.

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arXiv2020

Loops on the Celestial Sphere

We study the effect of loop corrections to conformal correlators on the celestial sphere at null infinity. We first analyze finite one-loop celestial amplitudes in pure Yang-Mills theory and Einstein gravity. We then turn to our main focus: infrared divergent loop amplitudes in planar $\mathcal{N}=4$ super Yang-Mills theory. We compute the celestial one-loop amplitude in dimensional regularization and show that it can be recast as an operator acting on the celestial tree-level amplitude. This extends to any loop order and the re-summation of all planar loops enables us to write down an expression for the all-loop celestial amplitude. Finally, we show that the exponentiated all-loop expression given by the BDS formula gets promoted on the celestial sphere to an operator acting on the tree-level conformal correlation function, thus yielding, the celestial BDS formula.

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arXiv2019

Meronic Einstein-Yang-Mills black hole in 5D and gravitational spin from isospin effect

We construct an analytic black hole solution in $SU(2)$ Einstein-Yang-Mills theory in five dimensions supporting a Meron field. The gauge field is proportional to a pure gauge and has a non-trivial topological charge. The would-be singularity at the Meron core gets shielded from the exterior by the black hole horizon. The metric has only one integration constant, namely, its ADM mass, which is shown to be finite once an appropriate boundary term is added to the action. The thermodynamics is also worked out, and a first-order phase transition, similar to the one occurring in the Reissner-Nordstr{ö}m case is identified. We also show that the solution produces a \mbox{\textit{spin from isospin effect}}, i.e., even though the theory is constructed out of bosons only, the combined system of a scalar field and this background may become fermionic. More specifically, we study scalar excitations in this purely bosonic background and find that the system describes fermionic degrees of freedom at spatial infinity. Finally, for the asymptotically $AdS_{5}$ case, we study its consequences in the context of the AdS/CFT correspondence.

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arXiv2017

Vortices with source, FQHE and nontrivial statistics in 2+1 dimensions

We investigate vortex soliton solutions in 2+1 dimensional scalar gauge theories, in the presence of source terms in the action. Concretely, this would be applied to anyons, as well as the Fractional Quantum Hall Effect (FQHE). We classify solitons for renormalizable potentials, as well as some nonrenormalizable examples that could be relevant for the FQHE. The non-Abelian case, specifically for theories with global non-Abelian symmetries, is also investigated, as is the non-relativistic limit of the above theories, when we get a modification of the Jackiw-Pi model, with an interesting new vortex solution. We explore the application to the ABJM model, as well as more general SYM-CS models in 2+1 dimensions.

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arXiv2016

(Non-adiabatic) string creation on nice slices in Schwarzschild black holes

Nice slices have played a pivotal role in the discussion of the black hole information paradox as they avoid regions of strong spacetime curvature and yet smoothly cut through the infalling matter and the outgoing Hawking radiation, thus, justifying the use of low energy field theory. To avoid information loss it has been argued recently, however, that local effective field theory has to break down at the horizon. To assess the extent of this breakdown in a UV complete framework we study string-theoretic effects on nice slices in Schwarzschild black holes. Our purpose is two-fold. First, we use nice slices to address various open questions and caveats of arXiv:1402.1486 where it was argued that boost-enhanced non-adiabatic string-theoretic effects at the horizon could provide a dynamical mechanism for the firewall. Second, we identify two non-adiabatic effects on nice slices in Schwarzschild black holes: pair production of open strings near the horizon enhanced by the presence of the infinite tower of highly excited string states and a late-time non-adiabatic effect intrinsic to nice slices.

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arXiv2014

On Type 0 Open String Amplitudes and the Tensionless Limit

The sum over planar multi-loop diagrams in the NS+ sector of type 0 open strings in flat spacetime has been proposed by Thorn as a candidate to resolve non-perturbative issues of gauge theories in the large $N$ limit. With $SU (N)$ Chan-Paton factors, the sum over planar open string multi-loop diagrams describes the 't Hooft limit $N\to \infty$ with $Ng_s^2$ held fixed. By including only planar diagrams in the sum the usual mechanism for the cancellation of loop divergences (which occurs, for example, among the planar and Möbius strip diagrams by choosing a specific gauge group) is not available and a renormalization procedure is needed. In this article the renormalization is achieved by suspending total momentum conservation by an amount $p\equiv \sum_i^n k_i\neq 0$ at the level of the integrands in the integrals over the moduli and analytically continuing them to $p=0$ at the very end. This procedure has been successfully tested for the 2 and 3 gluon planar loop amplitudes by Thorn. Gauge invariance is respected and the correct running of the coupling in the limiting gauge field theory was also correctly obtained. In this article we extend those results in two directions. First, we generalize the renormalization method to an arbitrary $n$-gluon planar loop amplitude giving full details for the 4-point case. One of our main results is to provide a fully renormalized amplitude which is free of both UV and the usual spurious divergences leaving only the physical singularities in it. Second, using the complete renormalized amplitude, we extract the high-energy scattering regime at fixed angle (tensionless limit). Apart from obtaining the usual exponential falloff at high energies, we compute the full dependence on the scattering angle which shows the existence of a smooth connection between the Regge and hard scattering regimes.

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arXiv2013

Conductivity in the gravity dual to massive ABJM and the membrane paradigm

In this paper we analyze the effect of the massive deformation of the ABJM model on the calculation of conductivity of the dual theory. We show that some of the difficulties presented by the dual geometry, in particular the construction of black holes therein, can be at least partially circumvented by adopting a membrane paradigm-like computation of the conductivity, which requires us to know just the effect of the deformation on the {\it horizon} of a black hole in AdS${}_{4}$. The deformation at the horizon itself is found by first deforming the flat space near the horizon, and then using the corresponding solution near the horizon as initial conditions for the Einstein's equations. We find the same result, showing an increase in conductivity, using two types of membrane paradigm computations.

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arXiv2013

A Note on High-Energy Scattering of Open Superstrings

We study the Regge and hard scattering limits of the one-loop amplitude for massless open string states in the type I theory. For hard scattering we find the exact coefficient multiplying the known exponential falloff in terms of the scattering angle, without relying on a saddle point approximation for the integration over the cross ratio. This bypasses the issues of estimating the contributions from flat directions, as well as those that arise from fluctuations of the gaussian integration about a saddle point. This result allows for a straightforward computation of the small- angle behavior of the hard scattering regime and we find complete agreement with the Regge limit at high momentum transfer, as expected.

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arXiv2011

The Open String Regge Trajectory and Its Field Theory Limit

We study the properties of the leading Regge trajectory in open string theory including the open string planar one-loop corrections. With SU(N) Chan-Paton factors, the sum over planar open string multi-loop diagrams describes the 't Hooft limit N\to\infty. Our motivation is to improve the understanding of open string theory at finite α' as a model of gauge theories. SU(N) gauge theories in D space-time dimensions are described by requiring open strings to end on a stack of N Dp-branes of space-time dimension D=p+1. The large N leading trajectory α(t)=1+α' t+Σ(t) can be extracted, through order g^2, from the s\to-\infty limit, at fixed t, of the four open string tree and planar loop diagrams. We analyze the t\to0 behavior with the result that Σ(t)\sim-Cg^2(-α' t)^{(D-4)/2}/(D-4). This result precisely tracks the 1-loop Reggeized gluon of gauge theory in D>4 space-time dimensions. In particular, for D\to4 it reproduces the known infrared divergences of gauge theory in 4 dimensions with a Regge trajectory behaving as -\ln(-α^\prime t). We also study Σ(t) in the limit t\to-\infty and show that, when D<8, it behaves as α^\prime t/(\ln(-α^\prime t))^γ, where γ>0 depends on D and the number of massless scalars. Thus, as long as 4<D<8, the 1-loop correction stays small relative to the tree trajectory for the whole range -\infty<t<0. Finally we present the results of numerical calculations of Σ(t) for all negative t.

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