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.

The mass scale M{s} of superstring theory is an arbitrary parameter that can be as low as few TeVs if the Universe contains large extra dimensions. We propose a search for the effects of Regge excitations of fundamental strings at the CERN Large Hadron Collider (LHC), in the process pp-->gamma+jet. The underlying parton process is dominantly the single photon production in gluon fusion, gg-->gammag, with open string states propagating in intermediate channels. If the photon mixes with the gauge boson of the baryon number, which is a common feature of D-brane quivers, the amplitude appears already at the string disk level. It is completely determined by the mixing parameter-and it is otherwise model (compactification) independent. Even for relatively small mixing, 100 fb{-1} of LHC data could probe deviations from standard model physics, at a 5sigma significance, for M{s} as large as 3.3 TeV.

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 → qq and qq ′ → 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 → 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 dt ∼ 100 pb −1 . 0 1 String Regge resonances in models with low string scale are also discussed in [8,9], while KK graviton exchange into the bulk, which appears at the next order in perturbation theory, is discussed in [8,10,11].

This paper provides both a detailed study of color-dependence of link homologies, as realized in physics as certain spaces of BPS states, and a broad study of the behavior of BPS states in general. We consider how the spectrum of BPS states varies as continuous parameters of a theory are perturbed. This question can be posed in a wide variety of physical contexts, and we answer it by proposing that the relationship between unperturbed and perturbed BPS spectra is described by a spectral sequence. These general considerations unify previous applications of spectral sequence techniques to physics, and explain from a physical standpoint the appearance of many spectral sequences relating various link homology theories to one another. We also study structural properties of colored HOMFLY homology for links and evaluate Poincaré polynomials in numerous examples. Among these structural properties is a novel "sliding" property, which can be explained by using (refined) modular S-matrix. This leads to the identification of modular transformations in Chern-Simons theory and 3d N = 2 theory via the 3d/3d correspondence. Lastly, we introduce the notion of associated varieties as classical limits of recursion relations of colored superpolynomials of links, and study their properties.