The U(1)s in the Finite N Limit of Orbifold Field Theories

We study theories generated by orbifolding the {\cal N}=4 super conformal U(N) Yang Mills theory with finite N, focusing on the r\^ole of the remnant U(1) gauge symmetries of the orbifold process. It is well known that the one loop beta functions of the non abelian SU(N) gauge couplings vanish in these theories. It is also known that in the large N limit the beta functions vanish to all order in perturbation theory. We show that the beta functions of the non abelian SU(N) gauge couplings vanish to two and three loop order even for finite N. This is the result of taking the abelian U(1) of U(N)=SU(N)xU(1) into account. However, the abelian U(1) gauge couplings have a non vanishing beta function. Hence, those theories are not conformal for finite N. We analyze the renormalization group flow of the orbifold theories, discuss the suppression of the cosmological constant and tackle the hierarchy problem in the non supersymmetric models.Comment: 2+35 pages, 2 figures, LaTe

Confinement in 4D Yang-Mills Theories from Non-Critical Type 0 String Theory

We study five dimensional non critical type 0 string theory and its correspondence to non supersymmetric Yang Mills theory in four dimensions. We solve the equations of motion of the low energy effective action and identify a class of solutions that translates into a confining behavior in the IR region of the dual gauge theories. In particular we identify a setup which is dual to pure SU(N) Yang-Mills theory. Possible flows of the solutions to the UV region are discussed. The validity of the solutions and potential sub-leading string corrections are also discussed.Comment: 25 pages, Latex. 1 figure. v2: refs. added, minor corrections, note added in section

Schnabl's L_0 Operator in the Continuous Basis

Following Schnabl's analytic solution to string field theory, we calculate the operators ${\cal L}_0,{\cal L}_0^\dagger$ for a scalar field in the continuous $\kappa$ basis. We find an explicit and simple expression for them that further simplifies for their sum, which is block diagonal in this basis. We generalize this result for the bosonized ghost sector, verify their commutation relation and relate our expressions to wedge state representations.Comment: 1+16 pages. JHEP style. Typos correcte

On the validity of the solution of string field theory

We analyze the realm of validity of the recently found tachyon solution of cubic string field theory. We find that the equation of motion holds in a non trivial way when this solution is contracted with itself. This calculation is needed to conclude the proof of Sen's first conjecture. We also find that the equation of motion holds when the tachyon or gauge solutions are contracted among themselves.Comment: JHEP style, 9+1 pages. Typos correcte

Marginal deformations in string field theory

We describe a method for obtaining analytic solutions corresponding to exact marginal deformations in open bosonic string field theory. For the photon marginal deformation we have an explicit analytic solution to all orders. Our construction is based on a pure gauge solution where the gauge field is not in the Hilbert space. We show that the solution itself is nevertheless perfectly regular. We study its gauge transformations and calculate some coefficients explicitly. Finally, we discuss how our method can be implemented for other marginal deformations.Comment: 23 pages. v2: Some paragraphs improved, typos corrected, ref adde

On the classical equivalence of superstring field theories

We construct mappings that send solutions of the cubic and non-polynomial open superstring field theories to each other. We prove that the action is invariant under the maps and that gauge orbits are mapped into gauge orbits. It follows that the perturbative spectrum around solutions is the same in both theories. The mappings also preserve the string field reality condition. We generalize to the cases of a non-BPS D-brane and of multi-D-brane systems. We analyze the recently found analytical solutions of the cubic action, both in the BPS sector and the non-BPS sector and show that they span a one parameter family of solutions with empty cohomology and identical action, which suggests that they are gauge equivalent. We write the gauge transformations relating these solutions explicitly. This seems to suggest that open superstring field theory is able to describe a vacuum solution even around a BPS D-brane.Comment: v2: Action proof revised, discussion improved, typos corrected, conclusions unchanged. 25 page

On surface states and star-subalgebras in string field theory

We elaborate on the relations between surface states and squeezed states. First, we investigate two different criteria for determining whether a matter sector squeezed state is also a surface state and show that the two criteria are equivalent. Then, we derive similar criteria for the ghost sector. Next, we refine the criterion for determining whether a surface state is in H_{\kappa^2}, the subalgebra of squeezed states obeying [S,K_1^2]=0. This enables us to find all the surface states of the H_{\kappa^2} subalgebra, and show that it consists only of wedge states and (hybrid) butterflies. Finally, we investigate generalizations of this criterion and find an infinite family of surface states subalgebras, whose surfaces are described using a "generalized Schwarz-Christoffel" mapping.Comment: 38 pages, 6 figures, JHEP style; typos corrected, ref. adde

Normalization anomalies in level truncation calculations

We test oscillator level truncation regularization in string field theory by calculating descent relations among vertices, or equivalently, the overlap of wedge states. We repeat the calculation using bosonic, as well as fermionic ghosts, where in the bosonic case we do the calculation both in the discrete and in the continuous basis. We also calculate analogous expressions in field level truncation. Each calculation gives a different result. We point out to the source of these differences and in the bosonic ghost case we pinpoint the origin of the difference between the discrete and continuous basis calculations. The conclusion is that level truncation regularization cannot be trusted in calculations involving normalization of singular states, such as wedge states, rank-one squeezed state projectors and string vertices.Comment: 1+20 pages, 6 figures. v2: Ref. added, typos correcte