Couplings of N=1 chiral spinor multiplets

We derive the action for n_L≥1 chiral spinor multiplets coupled to vector and scalar multiplets. We give the component form of the action, which contains gauge invariant mass terms for the antisymmetric tensors in the spinor superfield and additional Green–Schwarz couplings to vector fields. We observe that supersymmetry provides mass terms for the scalars in the spinor multiplet that do not arise from eliminating an auxiliary field. We construct the dual action by explicitly performing the duality transformations in superspace and give its component form.     

Scattering of massive open strings in pure spinor

In Park (2008) [4], it was proposed that the D-brane geometry could be produced by open string quantum effects. In an effort to verify the proposal, we consider scattering amplitudes involving massive open superstrings. The main goal of this paper is to set the ground for two-loop “renormalization” of an oriented open superstring on a D-brane and to strengthen our skill in the pure spinor formulation of a superstring, an effective tool for multi-loop string diagrams. We start by reviewing scattering amplitudes of massless states in the 2D component method of the NSR formulation. A few examples of massive string scattering are worked out. The NSR results are then reproduced in the pure spinor formulation. We compute the amplitudes using the unintegrated form of the massive vertex operator constructed by Berkovits and Chandia (2002) [15]. We point out that it may be possible to discover new Riemann type identities involving Jacobi ?-functions by comparing a NSR computation and the corresponding pure spinor computation.     

Classical superstring mechanics

We describe the classical mechanics of the superstring in both hamiltonian and lagrangian formulations, including massless external fields. The formulation is a modification of that of Green and Schwarz that allows supersymmetric Lorentz covariant quantization.     

The Character of Pure Spinors

The character of holomorphic functions on the space of pure spinors in 10, 11 and 12 dimensions is calculated. From this character formula, we derive in a manifestly covariant way various central charges which appear in the pure spinor formalism for the superstring. We also derive in a simple way the zero momentum cohomology of the pure spinor BRST operator for the D=10 and D=11 superparticle Mathematics Subject Classifications (2000): 81T30, 83E30, 83E50     

Review of AdS/CFT Integrability, Chapter II.3: Sigma Model, Gauge Fixing

This review is devoted to the classical integrability of the AdS ₅ × S⁵ superstring theory. It starts with a reminder of the corresponding action as a coset model. The symmetries of this action are then reviewed. The classical integrability is then considered from the lagrangian and hamiltonian points of view. The second part of this review deals with the gauge fixing of this theory. Finally, some aspects of the pure spinor formulation are also briefly reviewed.     

Four-dimensional supersymmetric black holes of type IIA superstring

We systematically construct a large class of four-dimensional supersymmetric black hole solutions of toroidally compactified type IIA superstring theory by explicitly solving the Killing spinor equations. They correspond to orthogonally intersecting configurations in ten dimensions. With the Kaluza-Klein monopole, they are parameterized by four charges and preserve of the N = 8 supersymmetry. We found a simple map to associate each charge with the corresponding Killing spinor constraints. The embedding of the N = 4 supersymmetry of a toroidally compactified heterotic string into the N = 8 supersymmetry of the IIA superstring was explicitly shown. We also found explicitly the configurations with only Ramond-Ramond charges, and those with both Neveu-Schwarz Neveu-Schwarz charges and Ramond-Ramond charges, including the dilaton and the internal metrics. The T-dual of these configurations were shown to satisfy the Killing spinor equations as well.     

Quantum field theory as effective BV theory from Chern–Simons

The general procedure for obtaining explicit expressions for all cohomologies of Berkovits' operator is suggested. It is demonstrated that calculation of BV integral for the classical Chern–Simons-like theory (Witten's OSFT-like theory) reproduces BV version of two-dimensional gauge model at the level of effective action. This model contains gauge field, scalars, fermions and some other fields. We prove that this model is an example of “singular” point from the perspective of the suggested method for cohomology evaluation. For arbitrary “regular” point the same technique results in AKSZ (Alexandrov, Kontsevich, Schwarz, Zaboronsky) version of Chern–Simons theory (BF theory) in accord with [N. Berkovits, Covariant quantization of the superparticle using pure spinors, JHEP 0109 (2001) 016, hep-th/0105050; N. Berkovits, ICTP lectures on covariant quantization of the superstring, hep-th/0209059; M. Movshev, A. Schwarz, On maximally supersymmetric Yang–Mills theories, Nucl. Phys. B 681 (2004) 324, hep-th/0311132; M. Movshev, A. Schwarz, Algebraic structure of Yang–Mills theory, hep-th/0404183].     

Single-photon exchange quasi-potentials ofN-particle systems

The covariant single-time approach of quantum field theory and perturbation theory are used to construct an explicit form of the electromagnetic interaction operator for mixedN-particle systems consisting of spinor and scalar particles. F. Skoriny State University, Gomelsk. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 13–25, September, 1997.     

Killing spinors for the bosonic string and Kaluza–Klein theory with scalar potentials

The paper consists mainly of two parts. In the first part, we obtain well-defined Killing spinor equations for the low-energy effective action of the bosonic string with the conformal anomaly term. We show that the conformal anomaly term is the only scalar potential that one can add into the action that is consistent with the Killing spinor equations. In the second part, we demonstrate that Kaluza–Klein theory can be gauged so that the Killing spinors are charged under the Kaluza–Klein vector. This gauging process generates a scalar potential with a maximum that gives rise to an AdS spacetime. We also construct solutions of these theories.     

A homogeneous multicomponent cosmological model with interacting spinor,scalar, and vector fields in the presence of dark energy

The evolution of a homogeneous multicomponent cosmological model with interacting spinor, vector, and scalar fields in the presence of dark energy described by the ideal liquid with the corresponding state equation is considered. The source of the vector and spinor fields is the kinetic energy of the inflation (scalar) field that is modeled by introduction of Lagrangians for the spinor and vector fields interacting with the scalar field through the squared gradient. A system of the dynamic Einstein–Proca–Klein–Fock and ideal liquid equations in the presence of interaction of the cosmological model components is solved. The role of individual components in the process of model evolution is elucidated.     

One-loop gauge anomaly in type-1 superstring theory

The vanishing of the hexagon gauge anomaly of type-I superstring was shown previously by Green and Schwarz in the case that the gauge group is SO(32). The result, as well as the finiteness f the one-loop amplitude, makes the superstring theory a candidate for the unified theory including gravity. The vanishing of the gauge anomaly can be established for all N-point functions. The one-loop gauge anomaly is shown to be absent if the gauge group is SO(32).     

Complete N-point superstring disk amplitude I. Pure spinor computation

In this paper the pure spinor formalism is used to obtain a compact expression for the superstring N  -point disk amplitude. The color-ordered string amplitude is given by a sum over (N−3)!$(N-3)!$ super-Yang–Mills subamplitudes multiplied by multiple Gaussian hypergeometric functions. In order to obtain this result, the cohomology structure of the pure spinor superspace is exploited to generalize the Berends–Giele method of computing super-Yang–Mills amplitudes. The method was briefly presented in Mafra et al. (2011) [1], and this paper elaborates on the details and contains higher-rank examples of building blocks and associated cohomology objects. But the main achievement of this work is to identify these field-theory structures in the pure spinor computation of the superstring amplitude. In particular, the associated set of basis worldsheet integrals is constructively obtained here and thoroughly investigated together with the structure and properties of the amplitude in Mafra et al. (2011) [2], arXiv:1106.2646 [hep-th].     

Cartan–Weyl Dirac and Laplacian Operators,Brownian Motions: The Quantum Potential and Scalar Curvature,Maxwell’s and Dirac-Hestenes Equations,and Supersymmetric Systems

We present the Dirac and Laplacian operators on Clifford bundles over space–time, associated to metric compatible linear connections of Cartan–Weyl, with trace-torsion, Q. In the case of nondegenerate metrics, we obtain a theory of generalized Brownian motions whose drift is the metric conjugate of Q. We give the constitutive equations for Q. We find that it contains Maxwell’s equations, characterized by two potentials, an harmonic one which has a zero field (Bohm-Aharonov potential) and a coexact term that generalizes the Hertz potential of Maxwell’s equations in Minkowski space.We develop the theory of the Hertz potential for a general Riemannian manifold. We study the invariant state for the theory, and determine the decomposition of Q in this state which has an invariant Born measure. In addition to the logarithmic potential derivative term, we have the previous Maxwellian potentials normalized by the invariant density. We characterize the time-evolution irreversibility of the Brownian motions generated by the Cartan–Weyl laplacians, in terms of these normalized Maxwell’s potentials. We prove the equivalence of the sourceless Maxwell equation on Minkowski space, and the Dirac-Hestenes equation for a Dirac-Hestenes spinor field written on Minkowski space provided with a Cartan–Weyl connection. If Q is characterized by the invariant state of the diffusion process generated on Euclidean space, then the Maxwell’s potentials appearing in Q can be seen alternatively as derived from the internal rotational degrees of freedom of the Dirac-Hestenes spinor field, yet the equivalence between Maxwell’s equation and Dirac-Hestenes equations is valid if we have that these potentials have only two components corresponding to the spin-plane. We present Lorentz-invariant diffusion representations for the Cartan–Weyl connections that sustain the equivalence of these equations, and furthermore, the diffusion of differential forms along these Brownian motions. We prove that the construction of the relativistic Brownian motion theory for the flat Minkowski metric, follows from the choices of the degenerate Clifford structure and the Oron and Horwitz relativistic Gaussian, instead of the Euclidean structure and the orthogonal invariant Gaussian. We further indicate the random Poincaré–Cartan invariants of phase-space provided with the canonical symplectic structure. We introduce the energy-form of the exact terms of Q and derive the relativistic quantum potential from the groundstate representation. We derive the field equations corresponding to these exact terms from an average on the invariant state Cartan scalar curvature, and find that the quantum potential can be identified with 1 / 12R(g), where R(g) is the metric scalar curvature. We establish a link between an anisotropic noise tensor and the genesis of a gravitational field in terms of the generalized Brownian motions. Thus, when we have a nontrivial curvature, we can identify the quantum nonlocal correlations with the gravitational field. We discuss the relations of this work with the heat kernel approach in quantum gravity. We finally present for the case of Q restricted to this exact term a supersymmetric system, in the classical sense due to E.Witten, and discuss the possible extensions to include the electromagnetic potential terms of Q     

The Quantum Consistency of the Ten-Dimensional Heterotic String Effective Action

The finiteness of superstring theory at each order in perturbation theory is considered with respect to the ten-dimensional effective action. The quantum consistency of the ten-dimensional superstring effective action is confirmed with an analysis of the perturbative expansion of the quartic sector. It is found to be compatible with the finiteness of reduced four-dimensional theory.Furthermore, implications for the validity of superstring perturbation theoryat lower energies is considered.     

Equivalence of two-loop superstring amplitudes in the pure spinor and Ramond-Neveu-Schwarz formalisms

The pure spinor formalism for the superstring has recently been used to compute massless four-point two-loop amplitudes in a manifestly super-Poincaré covariant manner. In this Letter, we show that when all four external states are Neveu-Schwarz states, the two-loop amplitude coincides with the Ramond-Neveu-Schwarz result.     

Space-time evolution induced by spinor fields with canonical and non-canonical kinetic terms

We study spinor field theories as an origin to induce space-time evolution. Self-interacting spinor fields with canonical and non-canonical kinetic terms are considered in a Friedman–Robertson–Walker universe. The deceleration parameter is calculated by solving the equation of motion and the Friedman equation, simultaneously. It is shown that the spinor fields can accelerate and decelerate the universe expansion. To construct realistic models we discuss the contributions from the dynamical symmetry breaking.     

Electron-positron pair and photon generation from vacuum in a de sitter space

Electron-positron pair and photon generation from vacuum is considered for a de Sitter space. The amplitude is calculated in the lowest order of perturbation theory with respect to the radiation interaction. The initial and final vacuum states of the quantized spinor field are taken as those of an adiabatic Bunch-Davis vacuum. The amplitude is shown to be zero, i.e., an adiabatic vacuum in a de Sitter space is stable with respect to radiation. Biya Technological Institute, Polzunov Altai State Technological University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 85–89, October, 1998.     

Worldsheet instantons and a null string limit of Born–Infeld theory

For a superstring theory in four spacetime dimensions, we propose a modification of the Born–Infeld action that possesses a well-defined tensionless limit. We interpret this as describing the effective target space dynamics of null strings on a D3-brane. We argue that such a modification can be induced by nonperturbative contributions from instantons in the worldsheet σ-model describing string propagation on the brane.     

The IR stability of de Sitter QFT: physical initial conditions

This work uses Lorentz-signature in-in perturbation theory to analyze the late-time behavior of correlators in time-dependent interacting massive scalar field theory in de Sitter space. We study a scenario recently considered by Krotov and Polyakov in which the coupling g turns on smoothly at finite time, starting from g = 0 in the far past where the state is taken to be the (free) Bunch–Davies vacuum. Our main result is that the resulting correlators (which we compute at the one-loop level) approach those of the interacting Hartle–Hawking state at late times. We argue that similar results should hold for other physically-motivated choices of initial conditions. This behavior is to be expected from recent quantum “no hair” theorems for interacting massive scalar field theory in de Sitter space which established similar results to all orders in perturbation theory for a dense set of states in the Hilbert space. Our current work (1) indicates that physically motivated initial conditions lie in this dense set, (2) provides a Lorentz-signature counter-part to the Euclidean techniques used to prove such theorems, and (3) provides an explicit example of the relevant renormalization techniques.