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

2021 ◽  
Vol 2021 (9) ◽  
Author(s):  
Carlo Maccaferri ◽  
Jakub Vošmera
Keyword(s):  
Hilbert Space ◽  
Mass Term ◽  
Open String ◽  
Bound State ◽  
Closed String ◽  
World Sheet ◽  
Effective Potentials ◽  
First Order ◽  
Blowing Up ◽  
Chiral Ring

Abstract 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.

DERIVING THE FOUR-STRING AND OPEN-CLOSED STRING INTERACTIONS FROM GEOMETRIC STRING FIELD THEORY

1990 ◽  
Vol 05 (04) ◽  
pp. 659-724 ◽  
Author(s):  
MICHIO KAKU
Keyword(s):  
Field Theory ◽  
String Field Theory ◽  
Geometric Theory ◽  
Open String ◽  
Bound State ◽  
Closed String ◽  
String Length ◽  
Light Cone Gauge ◽  
New Class ◽  
Coulomb Term

One of the baffling questions concerning the covariant open string field theory is why there are two distinct BRST theories and why the four-string interaction appears in one version but not the other. We solve this mystery by showing that both theories are gauge-fixed versions of a higher gauge theory, called the geometric string field theory, with a new field, a string vierbein [Formula: see text], which allows us to gauge the string length and σ-parametrization. By fixing the gauge, we can derive the “endpoint gauge” (the covariantized light cone gauge), the “midpoint gauge” of Witten, or the “interpolating gauge” with arbitrary string lengths. We show explicitly that the four-string interaction is a gauge artifact of the geometric theory (the counterpart of the four-fermion instantaneous Coulomb term of QED). By choosing the interpolating gauge, we produce a new class of four-string interactions which smoothly interpolate between the endpoint gauge and the midpoint gauge (where it vanishes). Similarly, we can extract the closed string as a bound state of the open string, which appears in the endpoint gauge but vanishes in the midpoint gauge. Thus, the four-string and open-closed string interactions do not have to be added to the action as long as the string vierbein is included.

scholarly journals Closed string deformations in open string field theory. Part II. Superstring

2021 ◽  
Vol 2021 (9) ◽  
Author(s):  
Carlo Maccaferri ◽  
Jakub Vošmera
Keyword(s):  
Hilbert Space ◽  
Perturbation Theory ◽  
Hilbert Spaces ◽  
Source Term ◽  
Open String ◽  
Closed String ◽  
Gauge Invariant ◽  
Gauge Fixing ◽  
Invariant Coupling ◽  
String State

Abstract This is the second paper of a series of three. We construct effective open-closed superstring couplings by classically integrating out massive fields from open superstring field theories coupled to an elementary gauge invariant tadpole proportional to an on-shell closed string state in both large and small Hilbert spaces, in the NS sector. This source term is well known in the WZW formulation and by explicitly performing a novel large Hilbert space perturbation theory we are able to characterize the first orders of the vacuum shift solution, its obstructions and the non-trivial open-closed effective couplings in closed form. With the aim of getting all order results, we also construct a new observable in the A∞ theory in the small Hilbert space which correctly provides a gauge invariant coupling to physical closed strings and which descends from the WZW open-closed coupling upon partial gauge fixing and field redefinition. Armed with this new A∞ observable we use tensor co-algebra techniques to efficiently package the whole perturbation theory necessary for computing the effective action and we give all order results for the open-closed effective couplings in the small Hilbert space.

scholarly journals NONLINEAR SCHRÖDINGER DYNAMICS OF MATRIX D-BRANES

2001 ◽  
Vol 16 (02) ◽  
pp. 209-250 ◽  
Author(s):  
NICK E. MAVROMATOS ◽  
RICHARD J. SZABO
Keyword(s):  
Kinetic Energy ◽  
Quantum Dynamics ◽  
Planck Equation ◽  
Open String ◽  
Bound State ◽  
Renormalization Group Equation ◽  
Total Kinetic Energy ◽  
Group Equation ◽  
World Sheet ◽  
Nonlinear Schrödinger

We formulate an effective Schrödinger wave equation describing the quantum dynamics of a system of D0-branes by applying the Wilson renormalization group equation to the world sheet partition function of a deformed σ-model describing the system, which includes the quantum recoil due to the exchange of string states between the individual D-particles. We arrive at an effective Fokker–Planck equation for the probability density with diffusion coefficient determined by the total kinetic energy of the recoiling system. We use Galilean invariance of the system to show that there are three possible solutions of the associated nonlinear Schrödinger equation depending on the strength of the open string interactions among the D-particles. When the open string energies are small compared to the total kinetic energy of the system, the solutions are governed by freely-propagating solitary waves. When the string coupling constant reaches a dynamically determined critical value, the system is described by minimal uncertainty wavepackets which describe the smearing of the D-particle coordinates due to the distortion of the surrounding space–time from the string interactions. For strong string interactions, bound state solutions exist with effective mass determined by an energy-dependent shift of the static BPS mass of the D0-branes.

scholarly journals Closed string deformations in open string field theory. Part I. Bosonic string

2021 ◽  
Vol 2021 (9) ◽  
Author(s):  
Carlo Maccaferri ◽  
Jakub Vošmera
Keyword(s):  
Field Theory ◽  
Star Product ◽  
Open String ◽  
Closed String ◽  
Field Theories ◽  
Tree Level ◽  
Bulk Deformation ◽  
Gauge Invariant ◽  
First Order ◽  
String Background

Abstract This is the first of a series of three papers on open string field theories based on Witten star product deformed with a gauge invariant open/closed coupling. This de- formation is a tree-level tadpole which destabilizes the initial perturbative vacuum. We discuss the existence of vacuum-shift solutions which cancel the tadpole and represent a new configuration where the initial D-brane system has adapted to the change in the closed string background. As an example we consider the bulk deformation which changes the compactification radius and, to first order in the deformation, we reproduce the shift in the mass of the open string KK modes from the new kinetic operator after the vacuum shift. We also discuss the possibility of taming closed string degenerations with the open string propagator in the simplest amplitude corresponding to two closed strings off a disk.

scholarly journals OPEN STRING ON SYMMETRIC PRODUCT

2001 ◽  
Vol 16 (04) ◽  
pp. 557-607 ◽  
Author(s):  
HIROYUKI FUJI ◽  
YUTAKA MATSUO
Keyword(s):  
Field Theory ◽  
String Field Theory ◽  
Klein Bottle ◽  
Open String ◽  
Closed String ◽  
Symmetric Product ◽  
World Sheet ◽  
Typical Structure ◽  
Light Cone Quantization ◽  
Twisted Boundary Conditions

We discuss some basic properties of the open string on the symmetric product which is supposed to describe the open string field theory in discrete light-cone quantization (DLCQ). We first derive the consistent twisted boundary conditions for Annulus/Möbius/Klein Bottle diagrams and give the explicit form of the corresponding amplitude. They have the interpretation as the long open (or closed) string amplitude but the world sheet topology viewed from the short string and from the long string is in general different. Boundary (cross-cap) states of the short string are classified into three categories, the boundary (cross-cap) states of the long string and the "joint" state which connects two strings. The partition function has the typical structure of the string field theory in DLCQ. Tadpole condition is also analyzed and gives a reasonable gauge group SO(213).

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

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Ashoke Sen
Keyword(s):  
Field Theory ◽  
String Theory ◽  
Effective Action ◽  
Open String ◽  
Closed String ◽  
World Sheet ◽  
Superstring Theory ◽  
Reality Condition ◽  
Instanton Contribution ◽  
Integration Cycle

Abstract 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.

scholarly journals On the quantization of folded strings in non-critical dimensions

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Jacob Sonnenschein ◽  
Dorin Weissman
Keyword(s):  
Scalar Curvature ◽  
Space Dimension ◽  
Massive Particle ◽  
Open String ◽  
Closed String ◽  
Target Space ◽  
Critical Dimensions ◽  
Complete Set ◽  
Rotating String ◽  
Folding Point

Abstract Classical rotating closed string are folded strings. At the folding points the scalar curvature associated with the induced metric diverges. As a consequence one cannot properly quantize the fluctuations around the classical solution since there is no complete set of normalizable eigenmodes. Furthermore in the non-critical effective string action of Polchinski and Strominger, there is a divergence associated with the folds. We overcome this obstacle by putting a massive particle at each folding point which can be used as a regulator. Using this method we compute the spectrum of quantum fluctuations around the rotating string and the intercept of the leading Regge trajectory. The results we find are that the intercepts are a = 1 and a = 2 for the open and closed string respectively, independent of the target space dimension. We argue that in generic theories with an effective string description, one can expect corrections from finite masses associated with either the endpoints of an open string or the folding points on a closed string. We compute explicitly the corrections in the presence of these masses.

scholarly journals KLT factorization of winding string amplitudes

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Jaume Gomis ◽  
Ziqi Yan ◽  
Matthew Yu
Keyword(s):  
Scattering Amplitudes ◽  
Open String ◽  
Closed String ◽  
Open Strings ◽  
Toroidal Compactifications ◽  
Quantum Numbers ◽  
String Amplitudes

Abstract We uncover a Kawai-Lewellen-Tye (KLT)-type factorization of closed string amplitudes into open string amplitudes for closed string states carrying winding and momentum in toroidal compactifications. The winding and momentum closed string quantum numbers map respectively to the integer and fractional winding quantum numbers of open strings ending on a D-brane array localized in the compactified directions. The closed string amplitudes factorize into products of open string scattering amplitudes with the open strings ending on a D-brane configuration determined by closed string data.

scholarly journals D-BRANE RECOIL MISLAYS INFORMATION

1998 ◽  
Vol 13 (07) ◽  
pp. 1059-1089 ◽  
Author(s):  
JOHN ELLIS ◽  
N. E. MAVROMATOS ◽  
D. V. NANOPOULOS
Keyword(s):  
Evolution Equations ◽  
Zero Mode ◽  
External Source ◽  
Closed String ◽  
The Other ◽  
Light Particle ◽  
World Sheet ◽  
Liouville Type ◽  
Dilute Gas ◽  
String State

We discuss the scattering of a light closed-string state off a D-brane, taking into account quantum recoil effects on the latter, which are described by a pair of logarithmic operators. The light particle and D-brane subsystems may each be described by a world sheet with an external source due to the interaction between them. This perturbs each subsystem away from criticality, which is compensated by dressing with a Liouville field whose zero mode we interpret as time. The resulting evolution equations for the D-brane and the closed string are of Fokker–Planck and modified quantum Liouville type, respectively. The apparent entropy of each subsystem increases as a result of the interaction between them, which we interpret as the loss of information resulting from nonobservation of the other entangled subsystem. We speculate on the possible implications of these results for the propagation of closed strings through a dilute gas of virtual D-branes.

Sign in / Sign up

Export Citation Format

Share Document