Membrane Dynamics in M(atrix) Theory

We analyze some of the kinematical and dynamical properties of flat infinite membrane solutions in the conjectured M theory proposed by Banks, Fischler, Shenker and Susskind. In particular, we compute the long range potential between membranes and anti-membranes, and between membranes and gravitons, and compare it with the supergravity results. We also discuss membranes with finite relative longitudinal velocities, providing some evidence for the eleven dimensional Lorentz invariance of the theory.Comment: 20 pages, harvma

NS5-branes, holography and CFT deformations

A few supergravity solutions representing configurations of NS5-branes admit exact conformal field theory (CFT) description. Deformations of these solutions should be described by exactly marginal operators of the corresponding theories. We briefly review the essentials of these constructions and present, as a new case, the operators responsible for turning on angular momentum.Comment: 6 pages, 2 figures, Proceedings contribution to the 9th Hellenic School on Elementary Particle Physics and Gravity}, Corfu, Greece, September 200

Dilatation operator or Hamiltonian?

We analyze the situation when the Hamiltonian in field theory can be replaced by the dilatation operator.Comment: 5 pages, contribution to Constituents, Fundamental Forces And Symmetries Of The Univers

String Network from M-theory

We study the three string junctions and string networks in Type IIB string theory by explicity constructing the holomorphic embeddings of the M-theory membrane that describe such configurations. The main feature of them such as supersymmetry, charge conservation and balance of tensions are derived in a more unified manner. We calculate the energy of the string junction and show that there is no binding energy associated with the junction.Comment: 16 pages, harvmac, 2 figures, references adde

Construction of BRST invariant states in G/HG/H WZNW models.

We study the cohomology arising in the BRST formulation of G/H gauged WZNW models, i.e. in which the states of the gauged theory are projected out from the ungauged one by means of a BRST condition. We will derive for a general simple group $H$ with arbitrary level, conditions for which the cohomology is non-trivial. We show, by introducing a small perturbation due to Jantzen, in the highest weights of the representations, how states in the cohomology, "singlet pairs", arise from unphysical states, "Kugo-Ojima quartets", as the perturbation is set to zero. This will enable us to identify and construct states in the cohomology. The ghost numbers that will occur are $\pm p$, with $p$ uniquely determined by the representations of the algebras involved. Our construction is given in terms of the current modes and relies on the explicit form of highest weight null-states given by Malikov, Feigen and Fuchs.Comment: 12 pages, late

Quantum phase transitions in cascading gauge theory

We study a ground state of N=1 supersymmetric SU(K+P) x SU(K) cascading gauge theory of Klebanov et.al [1,2] on R x S^3 at zero temperature. A radius of S^3 sets a compactification scale mu. An interplay between mu and the strong coupling scale Lambda of the theory leads to an interesting pattern of quantum phases of the system. For mu > mu_cSB=1.240467(8)Lambda the ground state of the theory is chirally symmetric. At mu=mu_cSB the theory undergoes the first-order transition to a phase with spontaneous breaking of the chiral symmetry. We further demonstrate that the chirally symmetric ground state of cascading gauge theory becomes perturbatively unstable at scales below mu_c=0.950634(5)mu_cSB. Finally, we point out that for mu < 1.486402(5)Lambda the stress-energy tensor of cascading gauge theory can source inflation of a closed Universe.Comment: 62 pages, 9 figure

Two loop partition function for large N pure Yang-Mills theory on a small three-sphere

We give a direct path-integral calculation of the partition function for pure 3+1 dimensional U(N) Yang-Mills theory at large N on a small three-sphere, up to two-loop order in perturbation theory. From this, we calculate the one-loop shift in the Hagedorn/deconfinement temperature for the theory at small volume, finding that it increases (in units of the inverse sphere radius) as we go to larger coupling (larger volume). Our results also allow us to read off the sum of one-loop anomalous dimensions for all operators with a given engineering dimension in planar Yang-Mills theory on R^4. As checks on our calculation, we reproduce both the Hagedorn shift and some of the anomalous dimension sums by independent methods using the results of hep-th/0412029 and hep-th/0408178. The success of our calculation provides a significant check of methods used in hep-th/0502149 to establish a first order deconfinement transition for pure Yang-Mills theory on a small three-sphere.Comment: 40 pages, 4 figures, harvma

Branes, Superpotentials and Superconformal Fixed Points

We analyze various brane configurations corresponding to field theories in three, four and five dimensions. We find brane configurations which correspond to three dimensional N=2 and four dimensional N=1 supersymmetric QCD theories with quartic superpotentials, in which what appear to be ``hidden parameters'' play an important role. We discuss the construction of five dimensional N=1 supersymmetric gauge theories and superconformal fixed points using branes, which leads to new five dimensional N=1 superconformal field theories. The same five dimensional theories are also used, in a surprising way, to describe new superconformal fixed points of three dimensional N=2 supersymmetric theories, which have both ``electric'' and ``magnetic'' Coulomb branches.Comment: 41 pages, 14 figures, harvmac bi