Implications of the spectrum of dynamically generated string tension theories

The string tension does not have to be put in by hand, it can be dynamically generated, as in the case when we formulate string theory in the modified measure formalism, and other formulations as well. Then string tension appears, but as an additional dynamical degree of freedom. It can be seen however that this string tension is not universal, but rather each string generates its own string tension, which can have a different value for each string. We also define a new Tension scalar background field which change locally the value of the string tension along the world sheets of the strings. When there are many strings with different string tensions this Tension field can be determined from the requirement of world sheet conformal invariance and for two types of string tensions depending on the relative sign of the tensions we obtain nonsingular cosmologies and warp space scenarios and when the two string tensions are positive, we obtain scenarios where the Hagedorn temperature is avoided in the early universe or in regions of warped space time where the string tensions become very big.

D-instantons, string field theory and two dimensional string theory

In [4] Balthazar, Rodriguez and Yin (BRY) computed the one instanton contribution to the two point scattering amplitude in two dimensional string theory to first subleading order in the string coupling. Their analysis left undetermined two constants due to divergences in the integration over world-sheet variables, but they were fixed by numerically comparing the result with that of the dual matrix model. If we consider n-point scattering amplitudes to the same order, there are actually four undetermined constants in the world-sheet approach. We show that using string field theory we can get finite unambiguous values of all of these constants, and we explicitly compute three of these four constants. Two of the three constants determined this way agree with the numerical result of BRY within the accuracy of numerical analysis, but the third constant seems to differ by 1/2. We also discuss a shortcut to determining the fourth constant if we assume the equality of the quantum corrected D-instanton action and the action of the matrix model instanton. This also agrees with the numerical result of BRY.

JT gravity limit of Liouville CFT and matrix model

In this paper we study a connection between Jackiw-Teitelboim (JT) gravity on two-dimensional anti de-Sitter spaces and a semiclassical limit of c < 1 two-dimensional string theory. The world-sheet theory of the latter consists of a space-like Liouville CFT coupled to a non-rational CFT defined by a time-like Liouville CFT. We show that their actions, disk partition functions and annulus amplitudes perfectly agree with each other, where the presence of boundary terms plays a crucial role. We also reproduce the boundary Schwarzian theory from the Liouville theory description. Then, we identify a matrix model dual of our two-dimensional string theory with a specific time-dependent background in c = 1 matrix quantum mechanics. Finally, we also explain the corresponding relation for the two-dimensional de-Sitter JT gravity.

D-instantons in Type IIA string theory on Calabi-Yau threefolds

Type IIA string theory compactified on a Calabi-Yau threefold has a hypermultiplet moduli space whose metric is known to receive non-perturbative corrections from Euclidean D2-branes wrapped on 3-cycles. These corrections have been computed earlier by making use of mirror symmetry, S-duality and twistorial description of quaternionic geometries. In this paper we compute the leading corrections in each homology class using a direct world-sheet approach without relying on any duality symmetry or supersymmetry. Our results are in perfect agreement with the earlier predictions.

Normalization of D-instanton amplitudes

D-instanton amplitudes suffer from various infrared divergences associated with tachyonic or massless open string modes, leading to ambiguous contribution to string amplitudes. It has been shown previously that string field theory can resolve these ambiguities and lead to unambiguous expressions for D-instanton contributions to string amplitudes, except for an overall normalization constant that remains undetermined. In this paper we show that string field theory, together with the world-sheet description of the amplitudes, can also fix this normalization constant. We apply our analysis to the special case of two dimensional string theory, obtaining results in agreement with the matrix model results obtained by Balthazar, Rodriguez and Yin.

The physical states of the Hybrid Formalism

String theory on AdS3 × S3 × $$ \mathbbm{T} $$ T 4 with one unit (k = 1) of NS-NS flux is considered in the hybrid formalism of Berkovits, Vafa & Witten (BVW). Using the free field realisation of the world-sheet theory at k = 1, we identify explicitly the BRST cohomology classes corresponding to some of the low-lying states of the dual CFT. In particular, we do this for the $$ \mathcal{N} $$ N = 4 superconformal generators of the symmetric orbifold theory, and we confirm these identifications by showing that the worldsheet correlators reproduce the expected dual CFT answer. Along the way we note that the physical vertex operators on the worldsheet have a simpler form if one works with a different, but equivalent, choice for the BRST operators relative to BVW.

Light like segment compactification and braneworlds with dynamical string tension

There is great interest in the construction of brane worlds, where matter and gravity are forced to be effective only in a lower dimensional surface, the brane . How these could appear as a consequence of string theory is a crucial question and this has been widely discussed. Here we will examine a distinct scenario that appears in dynamical string tension theories and where string tension is positive between two surfaces separated by a short distance and at the two surfaces themselves the string tensions become infinite, therefore producing an effective confinement of the strings and therefore of all matter and gravity to the space between these to surfaces, which is in fact a new type of stringy brane world scenario. The specific model studied is in the context of the modified measure formulation the string where tension appear as an additional dynamical degree of freedom and these tensions are not universal, but rather each string generates its own tension, which can have a different value for each string. We consider a new background field that can couple to these strings, the tension scalar is capable then of changing locally along the world sheet and then the value of the tension of the extended object changes accordingly. When many types of strings probing the same region of space are considered this tension scalar is constrained by the requirement of quantum conformal invariance. For the case of two types of strings probing the same region of space with different dynamically generated tensions, there are two different metrics, associated to the different strings, that have to satisfy vacuum Einsteins equations and the consistency of these two Einsteins equations determine the tension scalar. The universal metric, common to both strings generically does not satisfy Einsteins equation . The two metrics considered here are flat space in Minkowshi space and flat space after a special conformal transformation and the tension field behaves in such a way that strings are confined inside a light like Segment or alternatively as expanding Braneworlds where the strings are confined between two expanding bubbles separated by a very small distance at large times.

Closed string deformations in open string field theory. Part III. $$ \mathcal{N} $$ = 2 worldsheet localization

In this paper, which is the last of a series including [1, 2] we first verify that the two open-closed effective potentials derived in the previous paper from the WZW theory in the large Hilbert space and the A∞ theory in the small Hilbert space have the same vacuum structure. In particular, we show that mass-term deformations given by the effective (open)2-closed couplings are the same, provided the effective tadpole is vanishing to first order in the closed string deformation. We show that this condition is always realized when the worldsheet BCFT enjoys a global $$ \mathcal{N} $$ N = 2 superconformal symmetry and the deforming closed string belongs to the chiral ring in both the holomorphic and anti-holomorphic sector. In this case it is possible to explicitly evaluate the mass deformation by localizing the SFT Feynman diagrams to the boundary of world-sheet moduli space, reducing the amplitude to a simple open string two-point function. As a non-trivial check of our construction we couple a constant Kalb-Ramond closed string state to the OSFT on the D3–D(−1) system and we show that half of the bosonic blowing-up moduli become tachyonic, making the system condense to a bound state whose binding energy we compute exactly to second order in the closed string deformation, finding agreement with the literature.

A Penrose limit for type IIB AdS6 solutions

In this paper a Penrose limit is constructed for type IIB AdS6× S2× Σ supergravity solutions. These solutions are dual to five dimensional SCFTs related to (p,q) five brane webs, which can often be described in terms of long quiver gauge theories. The null geodesic from which the Penrose limit is constructed is localized at a unique point on the two dimensional Riemann surface Σ, where the AdS6 and S2 metric factors are extremal. The resulting pp-wave spacetime takes a universal form. The world sheet action of the Green-Schwarz string is quadratic in the light cone gauge and the spectrum of string excitations is obtained.

Cutkosky rules and unitarity (violation) in D-instanton amplitudes

In perturbative amplitudes in quantum field theory and string field theory, Cutkosky rule expresses the anti-hermitian part of a Feynman diagram in terms of sum over all its cut diagrams, and this in turn is used to prove unitarity of the theory. For D-instanton contribution to a string theory amplitude, the cutting rule needed for the proof of unitarity is somewhat different; we need to sum over only those cut diagrams for which all the world-sheet boundaries ending on some particular D-instanton lie on the same side of the cut. By working with the closed string effective action, obtained after integrating out the open string modes, we prove that the D-instanton amplitudes actually satisfy these cutting rules, provided the effective action is real. The violation of unitarity in the closed string sector of two dimensional string theory can be traced to the failure of this reality condition. In the critical superstring theory, multi-instanton and multi anti-instanton amplitudes satisfy the reality condition. Contribution to the amplitudes from the instanton anti-instanton sector satisfies the reality condition if we make a specific choice of integration cycle over the configuration space of string fields, whereas contribution due to the non-BPS D-instantons will need to either vanish or have an overall real normalization in order for it to give real contribution. We use Picard-Lefschetz theory to argue that these conditions are indeed satisfied in superstring theories.