Stephan Stieberger

The LHC string Hunter's companion

Abstract 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.

Threshold corrections to gauge couplings in orbifold compactifications

Abstract We derive the moduli-dependent threshold corrections to gauge couplings in toroidal orbifold compactifications. The underlying six-dimensional torus lattice of the heterotic string theory is not assumed — as in previous calculations — to decompose into a direct sum of a four-dimensional and a two-dimensional sublattice, with the latter lying in a plane left fixed by a set of orbifold twists. In this more general case the threshold corrections are no longer automorphic functions of the modular group, but of certain congruence subgroups of the modular group. These groups can also be obtained by studying the massless spectrum; moreover they have larger classes of automorphic functions. As a consequence, the threshold corrections cannot be uniquely determined by symmetry considerations and certain boundary conditions at special points in the moduli space, as was claimed in previous publications.

Dijet Signals for Low Mass Strings at the Large Hadron Collider

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 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. Data on pp-->directgamma + jet can provide corroboration for string physics at scales as high as 5 TeV.

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

Abstract We prove by explicit computation that 6-point matrix elements of D 4 R 4 and D 6 R 4 in N = 8 supergravity have non-vanishing single-soft scalar limits, and therefore these operators violate the continuous E 7 ( 7 ) symmetry. The soft limits precisely match automorphism constraints. Together with previous results for R 4 , this provides a direct proof that no E 7 ( 7 ) -invariant candidate counterterm exists below 7-loop order. At 7-loops, we characterize the infinite tower of independent supersymmetric operators D 4 R 6 , R 8 , φ 2 R 8 , … with n > 4 fields and prove that they all violate E 7 ( 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 8 R 4 has a non-linear supersymmetrization such that its single- and double-soft scalar limits are compatible with E 7 ( 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.

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.

LHC Phenomenology for String Hunters

Abstract 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 q q → q q and q q ′ → q q ′ , 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 p p → Z 0 + jet channel could deviate significantly from standard model predictions and (2) that the sizeable cross sections for Regge recurrences can allow a 6σ discovery for string scales as large as 3 TeV after about 1 year of LHC operation at s = 10 TeV and ∫ L d t ∼ 100 pb − 1 .

Supersymmetry Relations and MHV Amplitudes in Superstring Theory

Abstract 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 α ′ , as in the low-energy effective field theory describing the α ′ → 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 ⩽ 6 and deriving a compact expression for N = 7 .

Recursive method for n-point tree-level amplitudes in supersymmetric Yang-Mills theories

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.

Closed string amplitudes as single-valued open string amplitudes

We show that the single trace heterotic N-point tree-level gauge amplitude ANHET can be obtained from the corresponding type I amplitude ANI by the single-valued (sv) projection: ANHET=sv(ANI). This projection maps multiple zeta values to single-valued multiple zeta values. The latter represent a subclass of multiple zeta values originating from single-valued multiple polylogarithms at unity. Similar relations between open and closed string amplitudes or amplitudes of different string vacua can be established. As a consequence the α′-expansion of a closed string amplitude is dictated by that of the corresponding open string amplitude. The combination of single-valued projections, Kawai–Lewellen–Tye relations and Mellin correspondence reveal a unity of all tree-level open and closed superstring amplitudes together with the maximally supersymmetric Yang–Mills and supergravity theories.

Black hole formation and classicalization in ultra-Planckian 2 -> N scattering

We establish a connection between the ultra-Planckian scattering amplitudes in field and string theory and unitarization by black hole formation in these scattering processes. Using as a guideline an explicit microscopic theory in which the black hole represents a bound-state of many soft gravitons at the quantum critical point, we were able to identify and compute a set of perturbative amplitudes relevant for black hole formation. These are the tree-level N-graviton scattering S-matrix elements in a kinematical regime (called classicalization limit) where the two incoming ultra-Planckian gravitons produce a large number N of soft gravitons. We compute these amplitudes by using the Kawai-Lewellen-Tye relations, as well as scattering equations and string theory techniques. We discover that this limit reveals the key features of the microscopic corpuscular black hole N-portrait. In particular, the perturbative suppression factor of a N-graviton final state, derived from the amplitude, matches the non-perturbative black hole entropy when N reaches the quantum criticality value, whereas final states with different value of N are either suppressed or excluded by non-perturbative corpuscular physics. Thus we identify the microscopic reason behind the black hole dominance over other final states including non-black hole classical object. In the parameterization of the classicalization limit the scattering equations can be solved exactly allowing us to obtain closed expressions for the high-energy limit of the open and closed superstring tree-level scattering amplitudes for a generic number N of external legs. We demonstrate matching and complementarity between the string theory and field theory in different large-s and large-N regimes