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.

We explore the cosmological content of Salam-Sezgin six dimensional supergravity, and find a solution to the field equations in qualitative agreement with observation of distant supernovae, primordial nucleosynthesis abundances, and recent measurements of the cosmic microwave background. The carrier of the acceleration in the present de Sitter epoch is a quintessence field slowly rolling down its exponential potential. Intrinsic to this model is a second modulus which is automatically stabilized and acts as a source of cold dark matter, with a mass proportional to an exponential function of the quintessence field (hence realizing VAMP models within a String context). However, any attempt to saturate the present cold dark matter component in this manner leads to unacceptable deviations from cosmological data -a numerical study reveals that this source can account for up to about 7% of the total cold dark matter budget. We also show that (1) the model will support a de Sitter energy in agreement with observation at the expense of a miniscule breaking of supersymmetry in the compact space; (2) variations in the fine structure constant are controlled by the stabilized modulus and are negligible; (3) "fifth" forces are carried by the stabilized modulus and are short range; (4) the long time behavior of the model in four dimensions is that of a Robertson-Walker universe with a constant expansion rate (w = −1/3). Finally, we present a String theory background by lifting our six dimensional cosmological solution to ten dimensions.

We conjecture formulae of the colored superpolynomials for a class of twist knots K p where p denotes the number of full twists. The validity of the formulae is checked by applying differentials and taking special limits. Using the formulae, we compute both the classical and quantum super-A-polynomials for the twist knots with small values of p. The results support the categorified versions of the generalized volume conjecture and the quantum volume conjecture. Furthermore, we obtain the evidence that the Q-deformed Apolynomials can be identified with the augmentation polynomials of knot contact homology in the case of the twist knots.

The LHC program will include the identification of events with single prompt high-k ⊥ photons as probes of new physics. We show that this channel is uniquely suited to search for experimental evidence of TeV-scale open string theory. At the parton level, we analyze single photon production in gluon fusion, gg → γg, 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 (which is actually determined in the minimal theory) -and it is otherwise model-(compactification-) independent. We discuss the string signal cross sections as well as the QCD background. The present analysis takes into account the recently obtained decay widths of first Regge recurrences, which are necessary for more precise determination of these cross sections in the resonant region. A vital part of the background discussion concerns the minimization of misidentified π 0 's emerging from high-p ⊥ jets. We show that even for relatively small mixing, 100 fb −1 of LHC data could probe deviations from standard model physics associated with TeVscale strings at a 5σ significance, for M string as large as 2.3 TeV. It is also likely that resonant bumps could be observed with approximately the same signal-to-noise ratio.

Abstract:We study 4d N = 2 gauge theories with a co-dimension two full surface operator, which exhibit a fascinating interplay of supersymmetric gauge theories, equivariant Gromov-Witten theory and geometric representation theory. For pure Yang-Mills and N = 2 * theory, we describe a full surface operator as the 4d gauge theory coupled to a 2d N = (2, 2) gauge theory. By supersymmetric localizations, we present the exact partition functions of both 4d and 2d theories which satisfy integrable equations. In addition, the form of the structure constants with a semi-degenerate field in SL(N, R) WZNW model is predicted from one-loop determinants of 4d gauge theories with a full surface operator via the AGT relation.