arXiv subjects

Stephan Stieberger

Publications and source records attributed to Stephan Stieberger.

At least 55 records · Page 3Linked to original sources

arXiv2013

Polylogarithms, Multiple Zeta Values and Superstring Amplitudes

A formalism is provided to calculate tree amplitudes in open superstring theory for any multiplicity at any order in the inverse string tension. We point out that the underlying world-sheet disk integrals share substantial properties with color-ordered tree amplitudes in Yang-Mills field theories. In particular, we closely relate world-sheet integrands of open-string tree amplitudes to the Kawai-Lewellen-Tye representation of supergravity amplitudes. This correspondence helps to reduce the singular parts of world-sheet disk integrals -including their string corrections- to lower-point results. The remaining regular parts are systematically addressed by polylogarithm manipulations.

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arXiv2013

Superstring/Supergravity Mellin Correspondence in Grassmannian Formulation

We extend the recently established Mellin correspondence of supergravity and superstring amplitudes to the case of arbitrary helicity configurations. The amplitudes are discussed in the framework of Grassmannian varieties. We generalize Hodges' determinant to a function of two sets of independent coordinates and show that tree-level supergravity amplitudes can be obtained by contour integrations of both sets in separate Grassmannians while in superstring theory, one set of coordinates is identified with string vertex positions at the disk boundary and Mellin transformed into generalized hypergeometric functions of Mandelstam invariants.

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arXiv2013

Superstring Amplitudes as a Mellin Transform of Supergravity

At the tree level, the maximally helicity violating amplitudes of N gauge bosons in open superstring theory and of N gravitons in supergravity are known to have simple representations in terms of tree graphs. For superstrings, the graphs encode integral representations of certain generalized Gaussian hypergeometric functions of kinematic invariants while for supergravity, they represent specific kinematic expressions constructed from spinor-helicity variables. We establish a superstring/supergravity correspondence for this class of amplitudes, by constructing a mapping between the positions of gauge boson vertices at the disk boundary and the helicity spinors associated to gravitons. After replacing vertex positions by a larger set of N(N-3)/2 coordinates, the superstring amplitudes become (multiple) Mellin transforms of supergravity amplitudes, from the projective space into the dual Mellin space of N(N-3)/2 kinematic invariants. Similarly, inverse Mellin transforms transmute open superstrings into supergravity. We elaborate on the properties of multiple Mellin and inverse Mellin transforms in the framework of superstring/supergravity correspondence.

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arXiv2012

Maximally Helicity Violating Disk Amplitudes, Twistors and Transcendental Integrals

We obtain simple expressions for tree-level maximally helicity violating amplitudes of N gauge bosons from disk world-sheets of open superstrings. The amplitudes are written in terms of (N-3)! hypergeometric integrals depending on kinematic parameters, weighted by certain kinematic factors. The integrals are transcendental in a strict sense defined in this work. The respective kinematic factors can be succinctly written in terms of "dual" momentum twistors. The amplitudes are computed by using the prescription proposed by Berkovits and Maldacena.

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arXiv2011

A recursive method for SYM n-point tree amplitudes

We present a recursive method for super Yang-Mills color-ordered n-point tree amplitudes based on the cohomology of pure spinor superspace in ten space-time dimensions. The amplitudes are organized into BRST covariant building blocks with diagrammatic interpretation. Manifestly cyclic expressions (no longer than one line each) are explicitly given up to n=10 and higher leg generalizations are straightforward.

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arXiv2011

Complete N-Point Superstring Disk Amplitude I. Pure Spinor Computation

In this paper the pure spinor formalism is used to obtain a compact expression for the superstring N-point disk amplitude. The color ordered string amplitude is given by a sum over (N-3)! super Yang-Mills subamplitudes multiplied by multiple Gaussian hypergeometric functions. In order to obtain this result, the cohomology structure of the pure spinor superspace is exploited to generalize the Berends-Giele method of computing super Yang-Mills amplitudes. The method was briefly presented in [1], and this paper elaborates on the details and contains higher-rank examples of building blocks and associated cohomology objects. But the main achievement of this work is to identify these field-theory structures in the pure spinor computation of the superstring amplitude. In particular, the associated set of basis worldsheet integrals is constructively obtained here and thoroughly investigated together with the structure and properties of the amplitude in [2].

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arXiv2011

Complete N-Point Superstring Disk Amplitude II. Amplitude and Hypergeometric Function Structure

Using the pure spinor formalism in part I [1] we compute the complete tree-level amplitude of N massless open strings and find a striking simple and compact form in terms of minimal building blocks: the full N-point amplitude is expressed by a sum over (N-3)! Yang-Mills partial subamplitudes each multiplying a multiple Gaussian hypergeometric function. While the former capture the space-time kinematics of the amplitude the latter encode the string effects. This result disguises a lot of structure linking aspects of gauge amplitudes as color and kinematics with properties of generalized Euler integrals. In this part II the structure of the multiple hypergeometric functions is analyzed in detail: their relations to monodromy equations, their minimal basis structure, and methods to determine their poles and transcendentality properties are proposed. Finally, a Groebner basis analysis provides independent sets of rational functions in the Euler integrals.

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arXiv2011

Explicit BCJ Numerators from Pure Spinors

We derive local kinematic numerators for gauge theory tree amplitudes which manifestly satisfy Jacobi identities analogous to color factors. They naturally emerge from the low energy limit of superstring amplitudes computed with the pure spinor formalism. The manifestation of the color--kinematics duality is a consequence of the superstring computation involving no more than (n-2)! kinematic factors for the full color dressed n-point amplitude. The bosonic part of these results describe gluon scattering independent on the number of supersymmetries and captures any N^kMHV helicity configuration after dimensional reduction to D=4 dimensions.

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arXiv2011

Six Open String Disk Amplitude in Pure Spinor Superspace

The tree-level amplitude of six massless open strings is computed using the pure spinor formalism. The OPE poles among integrated and unintegrated vertices can be efficiently organized according to the cohomology of pure spinor superspace. The identification and use of these BRST structures and their interplay with the system of equations fulfilled by the generalized Euler integrals allow the full supersymmetric six-point amplitude to be written in compact form. Furthermore, the complete set of extended Bern-Carrasco-Johansson relations are derived from the monodromy properties of the disk world-sheet and explicitly verified for the supersymmetric numerator factors.

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arXiv2010

E7(7) constraints on counterterms in N=8 supergravity

We prove by explicit computation that 6-point matrix elements of D^4R^4 and D^6R^4 in N=8 supergravity have non-vanishing single-soft scalar limits, and therefore these operators violate the continuous E7(7) symmetry. The soft limits precisely match automorphism constraints. Together with previous results for R^4, this provides a direct proof that no E7(7)-invariant candidate counterterm exists below 7-loop order. At 7-loops, we characterize the infinite tower of independent supersymmetric operators D^4R^6, R^8, phi^2 R^8,... with n>4 fields and prove that they all violate E7(7) symmetry. This means that the 4-graviton amplitude determines whether or not the theory is finite at 7-loop order. We show that the corresponding candidate counterterm D^8R^4 has a non-linear supersymmetrization such that its single- and double-soft scalar limits are compatible with E7(7) up to and including 6-points. At loop orders 7, 8, 9 we provide an exhaustive account of all independent candidate counterterms with up to 16, 14, 12 fields, respectively, together with their potential single-soft scalar limits.

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arXiv2010

Direct Production of Lightest Regge Resonances

We discuss direct production of Regge excitations in the collisions of massless four-dimensional superstring states, focusing on the first excited level of open strings ending on D-branes extending into higher dimensions. We construct covariant vertex operators and identify ``universal'' Regge states with the internal parts either trivial or determined by the world-sheet SCFT describing superstrings propagating on an arbitrary Calabi-Yau manifold. We evaluate the amplitudes involving one such massive state and up to three massless ones and express them in the helicity basis. The most important phenomenological applications of our results are in the context of low-mass string (and large extra dimensions) scenarios in which excited string states are expected to be produced at the LHC as soon as the string mass threshold is reached in the center-of-mass energies of the colliding partons. In order to facilitate the use of partonic cross sections, we evaluate them and tabulate for all production processes: gluon fusion, quark absorbing a gluon, quark-antiquark annihilation and quark-quark scattering.

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arXiv2010

LHC Phenomenology for String Hunters

We consider extensions of the standard model based on open strings ending on D-branes, with gauge bosons due to strings attached to stacks of D-branes and chiral matter due to strings stretching between intersecting D-branes. Assuming that the fundamental string mass scale is in the TeV range and the theory is weakly coupled, we discuss possible signals of string physics at the Large Hadron Collider (LHC). In previous works, direct channel excitations of Regge recurrences in parton-parton scattering supplied the outstanding new signature. The present work considers the deviation from standard model expectations for the 4-fermion processes qq\to qq and qq' \to qq', in which the s-channel excitation of string resonances is absent. In this case, we find that Kaluza-Klein recurrences at masses somewhat less than the string scale generate effective 4-fermion contact terms which can significantly enhance the dijet R ratio above its QCD value of about 0.6. The simultaneous observation of a nearby resonant structure in the dijet mass spectrum would provide a "smoking gun" for TeV scale string theory. In this work, we also show that (1) for M_{string}<3.5 TeV, the rates for various topologies arising from the pp \to Z^0 + jet channel could deviate significantly from standard model predictions and (2) that the sizeable cross sections for Regge recurrences can allow a 6σdiscovery for string scales as large as 3 TeV after about 1 year of LHC operation at \sqrt{s} =10 TeV and \int L dt ~ 100 pb^{-1}.

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arXiv2010

Dijet signals for low mass strings at the LHC

We consider extensions of the standard model based on open strings ending on D-branes, with gauge bosons due to strings attached to stacks of D-branes and chiral matter due to strings stretching between intersecting D-branes. Assuming that the fundamental string mass scale is in the TeV range and the theory is weakly coupled, we discuss possible signals of string physics at the Large Hadron Collider (LHC). In such D-brane constructions, the dominant contributions to full-fledged string amplitudes for all the common QCD parton subprocesses leading to dijets are completely independent of the details of compactification, and can be evaluated in a parameter-free manner. We make use of these amplitudes evaluated near the first resonant pole to determine the discovery potential of LHC for the first Regge excitations of the quark and gluon. Remarkably, the reach of LHC after a few years of running can be as high as 6.8 TeV. Even after the first 100 pb^{-1} of integrated luminosity, string scales as high as 4.0 TeV can be discovered. For string scales as high as 5.0 TeV, observations of resonant structures in pp \to {\rm direct} γ+ jet can provide interesting corroboration for string physics at the TeV-scale.

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arXiv2010

String Phenomenology at the LHC

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arXiv2008

The LHC String Hunter's Companion

The mass scale of fundamental strings can be as low as few TeV/c^2 provided that spacetime extends into large extra dimensions. We discuss the phenomenological aspects of weakly coupled low mass string theory related to experimental searches for physics beyond the Standard Model at the Large Hadron Collider (LHC). We consider the extensions of the Standard Model based on open strings ending on D-branes, with gauge bosons due to strings attached to stacks of D-branes and chiral matter due to strings stretching between intersecting D-branes. We focus on the model-independent, universal features of low mass string theory. We compute, collect and tabulate the full-fledged string amplitudes describing all 2->2 parton scattering subprocesses at the leading order of string perturbation theory. We cast our results in a form suitable for the implementation of stringy partonic cross sections in the LHC data analysis. The amplitudes involving four gluons as well as those with two gluons plus two quarks do not depend on the compactification details and are completely model-independent. They exhibit resonant behavior at the parton center of mass energies equal to the masses of Regge resonances. The existence of these resonances is the primary signal of string physics and should be easy to detect. On the other hand, the four-fermion processes like quark-antiquark scattering include also the exchanges of heavy Kaluza-Klein and winding states, whose details depend on the form of internal geometry. They could be used as ``precision tests'' in order to distinguish between various compactification scenarios.

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arXiv2008

Complete Six-Gluon Disk Amplitude in Superstring Theory

We evaluate all next-to-maximal helicity violating (NMHV) six-gluon amplitudes in type I open superstring theory in four dimensions, at the disk level, to all orders in alpha'. Although the computation utilizes supersymmetric Ward identities, the result holds for all compactifications, even for those that break supersymmetry and is completely model-independent. Together with the maximally helicity violating (MHV) amplitudes presented in the previous work, our results provide the complete six-gluon disk amplitude.

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arXiv2007

Supersymmetry Relations and MHV Amplitudes in Superstring Theory

We discuss supersymmetric Ward identities relating various scattering amplitudes in type I open superstring theory. We show that at the disk level, the form of such relations remains exactly the same, to all orders in alpha', as in the low-energy effective field theory describing the alpha'-> 0 limit. This result holds in D=4 for all compactifications, even for those that break supersymmetry. We apply SUSY relations to the computations of N-gluon MHV superstring amplitudes, simplifying the existing results for N<7 and deriving a compact expression for N=7.

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arXiv2007

Four-dimensional String Compactifications with D-Branes, Orientifolds and Fluxes

This review article provides a pedagogical introduction into various classes of chiral string compactifications to four dimensions with D-branes and fluxes. The main concern is to provide all necessary technical tools to explicitly construct four-dimensional orientifold vacua, with the final aim to come as close as possible to the supersymmetric Standard Model. Furthermore, we outline the available methods to derive the resulting four-dimensional effective action. Finally, we summarize recent attempts to address the string vacuum problem via the statistical approach to D-brane models.

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