arXiv subjects
Publications and source records attributed to Martin Schnabl.
We present simple explicit formulae for the change of the $g$-function, boundary state, boundary spectrum and structure constants between the endpoints of short boundary RG flows at next-to-leading order. The formulae are derived using open string field theory and tested on integrable RG flows between conformal boundary states in unitary Virasoro minimal models.
We continue our analysis of open string field theory based on A-infinity-algebras obtained from Witten's theory by attaching stubs to the elementary vertex. Classical solutions of the new theory can be obtained from known analytic solutions in Witten's theory by applying a cohomomorphism. In a previous work, two such cohomomorphisms were found, one non-cyclic, obtained from the homological perturbation lemma and another cyclic one by geometric methods. Here we show that the two resulting maps are related by a combination of a gauge transformation and a term vanishing on-shell. In the second part of the paper we generalize the whole construction to non-BPZ even stubs, in particular sliver frame stubs. We discuss algebraic and geometric aspects and analyze the resulting conditions on the homotopy operator. Moreover, we explicitly calculate the first few orders of the new A-infinity-algebra solution for the tachyon vacuum in the sliver frame.
We consider condensation of nearly marginal matter tachyons in closed string field theory and observe that upon restricting to a subspace of states not containing the ghost dilaton, the on-shell value of the action is proportional to the shift of the central charge of the matter CFT. This correspondence lets us find a novel conformal perturbation theory formula for the next-to-leading order shift of the central charge for a generic theory, which we test on Zamolodchikov's flow between consecutive minimal models. Upon reintroduction of the dilaton couplings, it is plausible to have a vanishing value of the on-shell action.
There are various reasons why adding stubs to the vertices of open string field theory (OSFT) is interesting: Not only the stubs can tame certain singularities and make the theory more well-behaved, but also the new theory shares a lot of similarities with closed string field theory, which helps to improve our understanding of its structure and possible solutions. In this paper we explore two natural ways of implementing stubs into the framework of OSFT, resulting in an A-infinity-algebra giving rise to infinitely many vertices. We find two distinct consistent actions, both generated by a field redefinition, interestingly sharing the same equations of motion. In the last section we illustrate their relationship and physical meaning by applying our construction to nearly marginal solutions.
Conformal boundary conditions in two-dimensional conformal field theories are still mostly an uncharted territory. Even less is known about the relevant boundary deformations that connect them. A natural approach to the problem is via conformal perturbation theory, which however becomes quickly intractable. Using the formalism of open string field theory, we construct the corresponding classical solution, from which we can easily extract the boundary theory data. As a simple illustration we calculate the boundary degeneracy $g$ to next-to-leading order for a generic theory.
We study generic properties of string theory effective actions obtained by classically integrating out massive excitations from string field theories based on cyclic homotopy algebras of $A_\infty$ or $L_\infty$ type. We construct observables in the UV theory and we discuss their fate after integration-out. Furthermore, we discuss how to compose two subsequent integrations of degrees of freedom (horizontal composition) and how to integrate out degrees of freedom after deforming the UV theory with a new consistent interaction (vertical decomposition). We then apply our general results to the open bosonic string using Witten's open string field theory. There we show how the horizontal composition can be used to systematically integrate out the Nakanishi-Lautrup field from the set of massless excitations, ending with a non-abelian $A_\infty$-gauge theory for just the open string gluon. Moreover we show how the vertical decomposition can be used to construct effective open-closed couplings by deforming Witten OSFT with a tadpole given by the Ellwood invariant. Also, we discuss how the effective theory controls the possibility of removing the tadpole in the microscopic theory, giving a new framework for studying D-branes deformations induced by changes in the closed string background.
In a linear dilaton background, it has been argued that an unstable D-brane can decay to the tachyon vacuum without leaving behind a remnant of tachyon matter. Here we address the question of how the D-brane can decay to the tachyon vacuum when the tachyon vacuum does not support physical fluctuations. Using the formalism of open string field theory, we find that the tachyon vacuum {\it can} support fluctuations provided they are "hidden" as nonperturbative effects behind a pure gauge asymptotic series.
An outstanding problem in open bosonic string field theory is the existence of nontrivial classical solutions in its universal sector. Such solutions independent of the underlying CFT would be relevant for any background, but aside of the celebrated tachyon vacuum, no well behaved solutions have been found so far. In this work we revisit the problem using the old fashioned level truncation technique, but armed with much more sophisticated techniques and greater computer power. In particular, using the homotopy continuation method we construct all solutions at level 6 (or 5) with twist symmetry imposed (or not), and improve the viable ones by Newton's method to levels 24-30. Surprisingly, a handful of solutions survive. One of them is tantalizingly close to the elusive double brane solution, although the fits to infinite level seem to invalidate this conclusion. A better behaved solution matches unexpectedly the properties of a ghost brane. This does not contradict anything, since the solution violates the reality condition of string field theory. Relaxing SU(1,1) singlet condition two more exotic solutions with the rough characteristics of half brane and ghost half brane are found. For the tachyon vacuum, by explicit numerical computations up to level 30, we confirm the Gaiotto and Rastelli's prediction about the turning point of the tachyon potential minimum as a function of the level.
We show how conformal field theory topological defects can relate solutions of open string field theory for different boundary conditions. To this end we generalize the results of Graham and Watts to include the action of defects on boundary condition changing fields. Special care is devoted to the general case when nontrivial multiplicities arise upon defect action. Surprisingly the fusion algebra of defects is realized on open string fields only up to a (star algebra) isomorphism.
We construct a representation of the zero central charge Virasoro algebra using string fields in Witten's open bosonic string field theory. This construction is used to explore extensions of the KBc algebra and find novel algebraic solutions of open string field theory.
We use the recently constructed solution for marginal deformations by one of the authors, to analytically relate the BCFT modulus (lambda_BCFT) to the coefficient of the boundary marginal field in the solution (lambda_SFT). We explicitly find that the relation is not one to one and the same value of lambda_SFT corresponds to a pair of different lambda_BCFT 's: a "small" one, and a "large" one. The BCFT moduli space is fully covered, but the coefficient of the marginal field in the solution is not a good global coordinate on such a space.
Given a consistent choice of conformally invariant boundary conditions in a two dimensional conformal field theory, one can construct new consistent boundary conditions by deforming with a relevant boundary operator and flowing to the infrared, or by a marginal deformation. Open string field theory provides a very universal tool to discover and study such new boundary theories. Surprisingly, it also allows one to go in the reverse direction and to uncover solutions with higher boundary entropy. We will illustrate our results on the well studied example of Ising model.
Boundary states are given by appropriate linear combinations of Ishibashi states. Starting from any OSFT solution and assuming Ellwood conjecture we show that every coefficient of such a linear combination is given by an Ellwood invariant, computed in a slightly modified theory where it does not trivially vanish by the on-shell condition. Unlike the previous construction of Kiermaier, Okawa and Zwiebach, ours is linear in the string field, it is manifestly gauge invariant and it is also suitable for solutions known only numerically. The correct boundary state is readily reproduced in the case of known analytic solutions and, as an example, we compute the energy momentum tensor of the rolling tachyon from the generalized invariants of the corresponding solution. We also compute the energy density profile of Siegel-gauge multiple lump solutions and show that, as the level increases, it correctly approaches a sum of delta functions. This provides a gauge invariant way of computing the separations between the lower dimensional D-branes.
In this short talk we review basic ideas of string field theory with the emphasis on the recent developments. We show how without too much technicality one can look for analytic solutions to Witten's open string field theory. This is an expanded version of a talk given by the author over the last year at a number of occasions and notably at the conference "Selected Topics in Mathematical and Particle Physics" in honor of Prof. Jiri Niederle's 70th birthday.
The level-truncation analysis of open string field theory for a class of periodic marginal deformations indicates that a branch of solutions in Siegel gauge exists only for a finite range of values of the marginal field. The periodicity in the deformation parameter is thus obscure. We use the relation between gauge-invariant observables and the closed string tadpole on a disk conjectured by Ellwood to construct a map between the deformation parameter of the boundary conformal field theory and the parameter labeling classical solutions of open string field theory. We evaluate the gauge-invariant observables for the numerical solutions in Siegel gauge up to level 12 and find that our results qualitatively agree with the analysis by Sen using the energy-momentum tensor and are consistent with the picture that the finite range of the branch covers one fundamental domain of the periodic moduli space.
We study properties of a class of solutions of open string field theory which depend on a single holomorphic function F(z). We show that the energy of these solutions is well defined and is given by integer multiples of a single D-brane tension. Potential anomalies are discussed in detail. Some of them can be avoided by imposing suitable regularity conditions on F(z), while the anomaly in the equation of motion seems to require an introduction of the so called phantom term.
The WZW form of open superstring field theory has linearized gauge invariances associated with the BRST operator Q and the zero mode eta_0 of the picture minus-one fermionic superconformal ghost. We discuss gauge fixing of the free theory in a simple class of gauges using the Faddeev-Popov method. We find that the world-sheet ghost number of ghost and antighost string fields ranges over all integers, except one, and at any fixed ghost number, only a finite number of picture numbers appear. We calculate the propagators in a variety of gauges and determine the field-antifield content and the free master action in the Batalin-Vilkovisky formalism. Unlike the case of bosonic string field theory, the resulting master action is not simply related to the original gauge-invariant action by relaxing the constraint on the ghost and picture numbers.
Existence of open string field theory solutions describing configurations of multiple space-filling D-branes has been a subject of numerous speculations for quite some time. In this talk we present some new results giving further support to these ideas.