Abstract:
It has been shown that (2+1)-dimensional N=8 super Yang-Mills (SYM) theory with electric flux is related to (2+1)- dimensional noncommutative open string (NCOS) theory by `2-11' flip. This implies that the instanton process in SYM theory, which corresponds to D0-brane exchange (M-momentum transfer) between D2-branes, is dual to the KK momentum exchange in NCOS theory, which is perturbative process in nature. In order to confirm this, we obtain the effective action of probe M2-brane on the background of tilted M2-branes, which would correspond to the one-loop effective action of SYM theory with non-perturbative instanton corrections. Then we consider the dual process in NCOS theory, which is the scattering amplitude of the wound graviton off the D2-F1 bound state involving KK-momentum transfer in x^2-direction. Both of them give the same interaction terms. Remarkably they also have the same behavior on the nontrivial velocity dependence. All these strongly support the duality between those two theories with completely different nature.

Abstract:
Recently it was shown that NCOS theories are part of a ten-dimensional theory known as Non-relativistic Wound string theory. We clarify the sense in which gravity is present in this theory. We show that Wound string theory contains exceptional unwound strings, including a graviton, which mediate the previously discovered instantaneous long-range interactions, but are negligible as asymptotic states. Unwound strings also provide the expected collective coordinates for the transverse D-branes in the theory. These and other results are shown to follow both from a direct analysis of the effect of the NCOS limit on the parent string theory, and from the worldsheet formalism developed by Gomis and Ooguri, about which we make some additional remarks. We also devote some attention to supergravity duals, and in particular show that the open and closed strings of the theory are respectively described by short and long strings on the supergravity side.

Abstract:
We examine the T-duality relation between 1+1 NCOS and the DLCQ limit of type IIA string theory. We show that, as long as there is a compact dimension, one can meaningfully define an `NCOS' limit of IIB/A string theory even in the absence of D-branes (and even if there is no B-field). This yields a theory of closed strings with strictly positive winding, which is T-dual to DLCQ IIA/B without any D-branes. We call this the Type IIB/A Wound String Theory. The existence of decoupled sectors can be seen directly from the energy spectrum, and mirrors that of the DLCQ theory. It becomes clear then that all of the different p+1 NCOS theories are simply different states of this single Wound IIA/B theory which contain D-branes. We study some of the properties of this theory. In particular, we show that upon toroidal compactification, Wound string theory is U-dual to various Wrapped Brane theories which contain OM theory and the ODp theories as special states.

Abstract:
We explicitly compute the Compton amplitude for the scattering of a photon and a (massless) ``electron/positron'' at tree level and one loop, in a four-dimensional fermionic heterotic string model. We comment on the relationship between the amplitudes we compute in string theory and the corresponding ones in field theory.

Abstract:
High energy fixed angle scattering is studied in matrix string theory. The saddle point world sheet configurations, which give the dominant contributions to the string theory amplitude, are taken as classical backgrounds in matrix string theory. A one loop fluctuation analysis about the classical background is performed. An exact treatment of the fermionic and bosonic zero modes is shown to lead to all of the expected structure of the scattering amplitude. The ten dimensional Lorentz invariant kinematical structure is obtained from the fermion zero modes, and the correct factor of the string coupling constant is obtained from the abelian gauge field zero modes. Up to a numerical factor we reproduce, from matrix string theory, the high energy limit of the tree level, four graviton scattering amplitude.

Abstract:
We show that the NCOS (noncommutative open string) theories on torus $T^p$ ($p\leq 5$) are U-dual to matrix theory on torus with electric flux background. Under U-duality, the number of D-branes and the number of units of electric flux get interchanged. Furthermore under the same U-duality the decoupling limit taken in the NCOS theory maps to the decoupling limit taken in the matrix theory, thus ensure the U-duality between those two class of theories. We consider the energy needed for Higgsing process and some bound states with finite energy and find agreements in both theories.

Abstract:
We review high energy symmetries of string theory at both the fixed angle or Gross regime (GR) and the fixed momentum transfer or Regge regime (RR). We calculated in details high energy string scattering amplitudes at arbitrary mass levels for both regimes. We discovered infinite linear relations among fixed angle string amplitudes conjectured by Gross in 1988 from decoupling of high energy zero-norm states (ZNS), and infinite recurrence relations among Regge string amplitudes from Kummer function U and Appell function F. In the GR/RR regime, all high energy string amplitudes can be solved by these linear/recurrence relations so that all GR/RR string amplitudes can be expressed in terms of one single GR/RR string amplitude. In addition, we found an interesting link between string amplitudes of the two regimes, and discovered that at each mass level the ratios among fixed angle amplitudes can be extracted from Regge string scattering amplitudes. This result enables us to argue that the known SL(5,C) dynamical symmetry of the Appell function F is crucial to probe high energy spacetime symmetry of string theory. Keywords: Symmetries of strings, Hard string scattering amplitudes, Regge string scattering amplitudes, High energy limits, Zero norm states, Linear relations, Recurrence relations

Abstract:
We revisit the decoupling phenomenon of massless modes in the noncommutative open string (NCOS) theories. We check the decoupling by explicit computation in (2+1) or higher dimensional NCOS theories and recapitulate the validity of the decoupling to all orders in perturbation theory.

Abstract:
Using the recent proposal for the observables in open string field theory, we explicitly compute the coupling of closed string tachyon and massless states with the open string states up to level two. Using these couplings, we then calculate the tree level S-matrix elements of two closed string tachyons or two massless states in the open string field theory. Up to some contact terms, the results reproduce exactly the corresponding amplitudes in the bosonic string theory.

Abstract:
We study the correspondence between the linear matrix model and the interacting nonlinear string theory. Starting from the simple matrix harmonic oscillator states, we derive in a direct way scattering amplitudes of 2-dimensional strings, exhibiting the nonlinear equation generating arbitrary N-point tree amplitudes. An even closer connection between the matrix model and the conformal string theory is seen in studies of the symmetry algebra of the system.