I. Ya. Aref'eva

New Representation for String Field Solves the Consistency Problem for Open Superstring Field Theory

Abstract We modify Wittens action for the NSR superstring. Our proposal is based on the use of new “double-step” picture-changing operators. The modified action, in contrast to Wittens, generates N -point tree-level amplitudes which agree with the Koba-Nielsen amplitudes. The action is gauge invariant without any reference to a regularization and manifestly space-time supersymmetric. The algebra of the gauge transformations is closed and the classical equations of motion do not contain any picture-changing insertions.

Tachyon condensation in cubic superstring field theory

Abstract It has been conjectured that at the stationary point of the tachyon potential for the non-BPS D-brane or brane–anti-D-brane pair, the negative energy density cancels the brane tension. We study this conjecture using a cubic superstring field theory with insertion of a double-step inverse picture changing operator. We compute the tachyon potential at levels (1/2,1) and (2,6). In the first case we obtain that the value of the potential at the minimum is 97.5% of the non-BPS D-brane tension. Using a special gauge in the second case we get 105.8% of the tension.

Quantum contour field equations

Abstract The renormalization procedure for fields on a contour is considered. It is shown that in a quantum string-like equation for a non-abelian contour field the mass term has the correct sign.

Two-loop diagrams in noncommutative ϕ44 theory

Abstract Explicit two-loop calculations in noncommutative ϕ 4 4 theory are presented. It is shown that the model is two-loop renormalizable.

Background formalism for superstring field theory

Abstract In the framework of the background formalism we analyse possible versions of the Witten-type NSR superstring field theory. We find the picture for string fields to be uniquely fixed by the requirement that the perturbative classical solutions are well-defined. This uniquely defined picture and the corresponding action are different from the ones in Wittens theory and coincide with the ones proposed from different reasons in our previous paper. Following the same background method we calculate the tree-level scattering amplitudes for the new action and argue that in contrast to the ones in Wittens original theory, the amplitudes are singularity-free and hence there is no need to add any tree-level counterterms. We also prove the amplitudes to reproduce correctly the first quantized results.

On the p-adic summability of the anharmonic oscillator

Abstract Some remarkable arithmetic properties of the anharmonic oscillator are considered. The concept of the p-adic summability is discussed. For the ground-state energy of the anharmonic oscillator the p-adic summability is shown.

On the Adelic String Amplitudes

Abstract Some remarkable properties of the adelic string amplitudes for the physical domain of the Mandelstam variables are considered. It is shown that the p-adic four-point functions are always negative. Also, a formula is obtained which expresses the product of moduli of the p-adic amplitudes and the Veneziano amplitude in terms of the zeta functions. This product is absolutely convergent unlike the divergent product of these amplitudes without moduli, recently considered by Freund and Witten. Using the zeta function representation, p-adic interpolation of the Veneziano amplitude is also considered.

Quantum group particles and non-archimedean geometry

Abstract The classical and quantum mechanics on the quantum plane are discussed. They correspond to q-deformation and h -q- deformations of the usual mechanics, respectively. A particle on the quantum line as the simplest example of such a kind of system is investigated in more detail. A new phenomenon occurs even for the free particle, namely, the mass for a free particle on the quantum line is not a number but a non-commutative element. Some relations between q-deformed quantum mechanics and p-adic quantum mechanics are also presented.

Renormalization and phase transition in the quantum ofCPN−1 model (D=2,3)

Abstract We prove in the framework of the 1/N expansion the ultraviolet renormalizibility of the ofCPN−1 model when D = 2, 3. It is shown that when D = 2 the model gains infrared divergences in higher orders of 1/N. When D = 3, the phase transition of second order occurs: above the critical points there exist N massive scalar charged particles and one particle corresponding to the massless isoscalar vector field, but below it there exist only N − 1 massless particles.

Non-extremal intersecting p-branes in various dimensions☆

Abstract Non-extremal intersecting p-brane solutions of gravity coupled with several antisymmetric fields and dilatons in various space-time dimensions are constructed. The construction uses the same algebraic method of finding solutions as in the extremal case and modified “no-force” conditions. We justify the “deformation” prescription. It is shown that the non-extremal intersecting p-brane solutions satisfy the harmonic superposition rule and intersections of non-extremal p-branes are specified by the same characteristic equations for the incidence matrices as for the extremal p-branes. We show that S -duality holds for non-extremal p-brane solutions. Generalized T -duality takes place under additional restrictions to the parameters of the theory, which are the same as in the extremal case.