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

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.

Double-soft behavior of massless closed strings interacting with any number of closed string tachyons

We calculate the simultaneous double-soft limit of two massless closed strings scattering with any number of closed string tachyons to the subleading order at the tree level. The limit factorizes the scattering amplitude into a double-soft factor multiplying the pure tachyon subamplitude, suggesting a universal double-soft theorem for the massless closed string. We confirm an existing result for the double-soft graviton in an on-shell equivalent, but different form, while also establishing the double-soft factorization behavior of the string dilaton and of the Kalb-Ramond state, as well as the mixed graviton-dilaton case. We also show that the simultaneous and consecutive double-soft theorems are consistent with each other. We furthermore provide a complete field theory diagrammatic view on our result, which enables us in particular to establish a four-point interaction vertex for two tachyons and two massless closed string states, as well as the missing in field theory of three-point interaction of two massless closed string state and one tachyon.

SEMICLASSICAL (QFT) AND QUANTUM (STRING) ROTATING BLACK HOLES AND THEIR EVAPORATION: NEW RESULTS

Combination of both quantum field theory (QFT) and string theory in curved backgrounds in a consistent framework, the string analogue model, allows us to provide a full picture of the Kerr–Newman black hole and its evaporation going beyond the current picture. We compute the quantum emission cross-section of strings by a Kerr–Newman black hole (KNbh). It shows the black hole emission at the Hawking temperature T sem in the early stage of evaporation and the new string emission featuring a Hagedorn transition into a string state of temperature Ts at the last stages. New bounds on J and Q emerge in the quantum string regime (besides the known ones of the classical/semiclassical QFT regime). The last state of evaporation of a semiclassical Kerr–Newman black hole with mass M > m Pl , angular momentum J and charge Q is a string state of temperature Ts, string mass Ms, J = 0 and Q = 0, decaying as usual quantum strings do into all kinds of particles. (Naturally, in this framework, there is no loss of information, (there is no paradox at all).) We compute the string entropy Ss(m, j) from the microscopic string density of states of mass m and spin mode j, ρ(m, j). (Besides the Hagedorn transition at Ts) we find for high j (extremal string states j → m2α′c), a new phase transition at a temperature [Formula: see text], higher than Ts. By precisely identifying the semiclassical and quantum (string) gravity regimes, we find a new formula for the Kerr black hole entropy S sem (M, J), as a function of the usual Bekenstein–Hawking entropy [Formula: see text]. For M ≫ m Pl and J < GM2/c, [Formula: see text] is the leading term, but for high angular momentum, (nearly extremal case J = GM2/c), a gravitational phase transition operates and the whole entropy S sem is drastically different from the Bekenstein–Hawking entropy [Formula: see text]. This new extremal black hole transition occurs at a temperature T sem J = (J/ℏ)T sem , higher than the Hawking temperature T sem .

D-BRANE RECOIL MISLAYS INFORMATION

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.

Rigid-Plastic Approximations for Predicting Plastic Deformation of Cylindrical Shells Subject to Dynamic Loading

A theoretical approach was developed for predicting the plastic deformation of a cylindrical shell subject to asymmetric dynamic loads. The plastic deformation of the leading generator of the shell is found by solving for the transverse deflections of a rigid-plastic beam/string-on-foundation. The axial bending moment and tensile force in the beam/string are equivalent to the longitudinal bending moments and membrane forces of the shell, while the plastic foundation force is equivalent to the shell circumferential bending moment and membrane resistances. Closed-form solutions for the transient and final deformation profile of an impulsive loaded shell when it is in a “string” state were derived using the eigenfunction expansion method. These results were compared to DYNA 3D predictions. The analytical predictions of the transient shell and final centerline deflections were within 25% of the DYNA 3D results.