Determining the global minimum of Higgs potentials via Groebner bases - applied to the NMSSM

Determining the global minimum of Higgs potentials with several Higgs fields like the next-to-minimal supersymmetric extension of the Standard Model (NMSSM) is a non-trivial task already at the tree level. The global minimum of a Higgs potential can be found from the set of all its stationary points defined by a multivariate polynomial system of equations. We introduce here the algebraic Groebner basis approach to solve this system of equations. We apply the method to the NMSSM with CP conserving as well as CP violating parameters. The results reveal an interesting stationary-point structure of the potential. Requiring the global minimum to give the electroweak symmetry breaking observed in Nature excludes large parts of the parameter space.Comment: 10 pages, 2 figure

Siegel Gauge in Vacuum String Field Theory

We study the star algebra of ghost sector in vacuum string field theory (VSFT). We show that the star product of two states in the Siegel gauge is BRST exact if we take the BRST charge to be the one found in hep-th/0108150, and the BRST exact states are nil factors in the star algebra. By introducing a new star product defined on the states in the Siegel gauge, the equation of motion of VSFT is characterized as the projection condition with respect to this new product. We also comment on the comma form of string vertex in the ghost sector.Comment: 13 pages, lanlmac; v3: comment adde

Ghost Kinetic Operator of Vacuum String Field Theory

Using the data of eigenvalues and eigenvectors of Neumann matrices in the 3-string vertex, we prove analytically that the ghost kinetic operator of vacuum string field theory obtained by Hata and Kawano is equal to the ghost operator inserted at the open string midpoint. We also comment on the values of determinants appearing in the norm of sliver state.Comment: 19 pages, 1 figure, lanlmac; v2: typos correcte

Ratio of Tensions from Vacuum String Field Theory

We show analytically that the ratio of the norm of sliver states agrees with the ratio of D-brane tensions. We find that the correct ratio appears as a twist anomaly.Comment: 13 pages, lanlmac; version to appear in JHE

Wedge states in string field theory

The wedge states form an important subalgebra in the string field theory. We review and further investigate their various properties. We find in particular a novel expression for the wedge states, which allows to understand their star products purely algebraically. The method allows also for treating the matter and ghost sectors separately. It turns out, that wedge states with different matter and ghost parts violate the associativity of the algebra. We introduce and study also wedge states with insertions of local operators and show how they are useful for obtaining exact results about convergence of level truncation calculations. These results help to clarify the issue of anomalies related to the identity and some exterior derivations in the string field algebra.Comment: 40 pages, 9 figures, v3: section 3.3 rewritten, few other corrections, set in JHEP styl

Stretched strings in tachyon condensation models

In this note, we consider the two derivative truncation of boundary string field theory for unstable D9 branes in Type IIA string theory. We construct multiples of the stable codimension 1 solitons that correspond to stacks of D8 branes. We find the fluctuation modes that correspond to open strings stretching between the branes, and find that their masses are consistent with the string tension. We show that these modes are localized halfway between the branes and that their width is independent of the brane separation.Comment: 12 pages, LaTeX; v2, references adde

The Tachyon Potential in the Sliver Frame

We evaluate the tachyon potential in the Schnabl gauge through off-shell computations in the sliver frame. As an application of the results of our computations, we provide a strong evidence that Schnabl's analytic solution for tachyon condensation in open string field theory represents a saddle point configuration of the full tachyon potential. Additionally we verify that Schnabl's analytic solution lies on the minimum of the effective tachyon potential.Comment: v1: 19 pages, 1 figure, 1 table; v2: 20 pages, 1 figure, 2 tables, 1 reference added, comments added; v3: 21 pages, 1 figure, 2 tables, 4 references added, comments adde

Experimental String Field Theory

We develop efficient algorithms for level-truncation computations in open bosonic string field theory. We determine the classical action in the universal subspace to level (18,54) and apply this knowledge to numerical evaluations of the tachyon condensate string field. We obtain two main sets of results. First, we directly compute the solutions up to level L=18 by extremizing the level-truncated action. Second, we obtain predictions for the solutions for L > 18 from an extrapolation to higher levels of the functional form of the tachyon effective action. We find that the energy of the stable vacuum overshoots -1 (in units of the brane tension) at L=14, reaches a minimum E_min = -1.00063 at L ~ 28 and approaches with spectacular accuracy the predicted answer of -1 as L -> infinity. Our data are entirely consistent with the recent perturbative analysis of Taylor and strongly support the idea that level-truncation is a convergent approximation scheme. We also check systematically that our numerical solution, which obeys the Siegel gauge condition, actually satisfies the full gauge-invariant equations of motion. Finally we investigate the presence of analytic patterns in the coefficients of the tachyon string field, which we are able to reliably estimate in the L -> infinity limit.Comment: 37 pages, 6 figure

Star Algebra Projectors

Surface states are open string field configurations which arise from Riemann surfaces with a boundary and form a subalgebra of the star algebra. We find that a general class of star algebra projectors arise from surface states where the open string midpoint reaches the boundary of the surface. The projector property of the state and the split nature of its wave-functional arise because of a nontrivial feature of conformal maps of nearly degenerate surfaces. Moreover, all such projectors are invariant under constant and opposite translations of their half-strings. We show that the half-string states associated to these projectors are themselves surface states. In addition to the sliver, we identify other interesting projectors. These include a butterfly state, which is the tensor product of half-string vacua, and a nothing state, where the Riemann surface collapses.Comment: 65 pages, 23 figures, LaTe

Dressed Sliver solutions in Vacuum String Field Theory

We consider a new class of solutions (dressed slivers) in Vacuum String Field Theory, which represent D25-branes. For each dressed sliver we introduce a deformation parameter and define a family of states which are characterized by new abelian star-subalgebras. We show that this deformation parameter can be used as a regulator: it allows us to define for each such solution a finite norm and energy density. Finally we show how to generalize these results to parallel coincident and to lower dimensional branes.Comment: 39 pages, JHEP style. v2:minor corrections, references adde