Functional equation for the string effective action

A functional equation for the purely gravitational part of the string effective action is found. Among its solutions are the extended Euler densities and products of Wely tensors. A possible recipe for the Ricci temrs is given.     

The effective action of a BPS Alice string

Recently a BPS Alice string has been found in a \(U(1)\times SO(3)\) gauge theory coupled with three charged complex scalar fields in the triplet representation (in JHEP 1709:046 arXiv:1703.08971 [hep-th], 2017). It is a half BPS state preserving a half of the supercharges when embedded into a supersymmetric gauge theory. In this paper, we study zero modes of a BPS Alice string. After presenting U(1) and translational zero modes, we construct the effective action of these modes. In contrast to a previous analysis of the conventional Alice string for which only large distance behaviors are known, we can exactly perform a calculation in the full space thanks to the BPS properties.     

Evidence for nonperturbative string symmetries

String theory appears to admit a group of discrete field transformations — calledS dualities — as exact nonperturbative quantum symmetries. Mathematically, they are rather analogous to the better-knownT duality symmetries, which hold perturbatively. In this Letter the evidence forS duality is reviewed and some speculations are presented.     

The local effective action for two-dimensional supergravity

We obtained the local effective actions for (1,0) and (0,1) supergravity. They were shown to be equivalent to the non-local supergravity actions.     

Hidden symmetries and Killing tensors

Just as a Killing vector of the kinetic energy metric of a classical mechanical system can generate a symmetry of the system (an “obvious” symmetry), and thus a constant of the motion, so can a Killing tensor generate a symmetry and a constant of the motion. In the latter case the symmetry is “hidden”: for example the well-known hidden symmetries for a single particle moving under an inverse-square central force, and for the harmonic oscillator, arise in this way.     

Field redefinition dependence of the low energy string effective action

We consider the effect of field redefinitions on the general form of the torsion dependent terms in theO(R) ³ string action.     

Unique effective action in two-dimensional quantum gravity with nonlocal action

The gauge dependence of the effective action in two-dimensional induced quantum gravity is investigated. A unique effective action is found, and its dependence on the metric of the configuration space is studied.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 97–100, January, 1992.     

The T-dual symmetries of a bosonic string

We investigate whether the symmetry transformations of a bosonic string are connected by T-duality. We start with a standard closed string theory. We continue with a modified open string theory, modified to preserve the symmetry transformations possessed by the closed string theory. Because the string theory is conformally invariant world-sheet field theory, in order to find the transformations which preserve the physics, one has to demand the isomorphism between the conformal field theories corresponding to the initial and the transformed field configurations. We find the symmetry transformations corresponding to the similarity transformation of the energy-momentum tensor, and find that their generators are T-dual. Particularly, we find that the general coordinate and local gauge transformations are T-dual, so we conclude that T-duality in addition to the well-known exchanges, transforms symmetries of the initial and its T-dual theory into each other.     

General symmetries of a string fluid space-time

It is shown that a string fluid is the simplest anisotropic fluid with vanishing heat flux. Furthermore it has the property that the Ricci tensor is obtained from the energy momentum tensor, and vice versa, if one interchanges the fluid variables. We use previous works on the collineations of anisotropic fluids, which include the string fluid as a particular case, to compute the kinematic and the dynamic effects of certain collineations of a string fluid. It is found that the possible spacetimes, which can carry a string fluid, are severely restricted and the possible string fluids in spacetimes, which can admit them are more or less fixed. We recover previous results on the effect of symmetries in string fluid spacetimes and get many new ones, for example the matter inheritance collineations. The study and the results are presented in a systematic manner, which allows the comprehension and the comparison of the restrictions imposed by each collineation. Finally one can use the same method of work for a systematic study of similar problems.     

Hidden symmetries in minimal five-dimensional supergravity

We study the hidden symmetries arising in the dimensional reduction of d=5, supergravity to three dimensions. Extending previous partial results for the bosonic part, we give a derivation that includes fermionic terms, shedding light on the appearance of the local hidden symmetry SO(4) in the reduction.     

Dynamical approach to conformal gravity and the bosonic string effective action

We show that a theory invariant under the full local conformal group in a coset realization contains naturally the massless degrees of freedom of the closed bosonic string. This effective theory is alternative to the bosonic part of SupergravityN=1 as given by Manton and Chapline [4].     

Hidden symmetries of higher-dimensional rotating black holes

We demonstrate that the rotating black holes in an arbitrary number of dimensions and without any restrictions on their rotation parameters possess the same hidden symmetry as the four-dimensional Kerr metric. Namely, besides the spacetime symmetries generated by the Killing vectors they also admit the (antisymmetric) Killing-Yano and symmetric Killing tensors.     

Hidden symmetries of integrable conformal mechanical systems

We split the generic conformal mechanical system into a “radial” and an “angular” part, where the latter is defined as the Hamiltonian system on the orbit of the conformal group, with the Casimir function in the role of the Hamiltonian. We reduce the analysis of the constants of motion of the full system to the study of certain differential equations on this orbit. For integrable mechanical systems, the conformal invariance renders them superintegrable, yielding an additional series of conserved quantities originally found by Wojciechowski in the rational Calogero model. Finally, we show that, starting from any N=4 supersymmetric “angular” Hamiltonian system one may construct a new system with full N=4 superconformal D(1,2;α) symmetry.     

High-energy zero-norm states and symmetries of string theory

High-energy limit of zero-norm states in the old covariant first quantized spectrum of the 26D open bosonic string, together with the assumption of a smooth behavior of string theory in this limit, are used to derive infinitely many linear relations among the leading high-energy, fixed-angle behavior of four-point functions of different string states. As a result, ratios among all high-energy scattering amplitudes of four arbitrary string states can be calculated algebraically and the leading order amplitudes can be expressed in terms of that of four tachyons as conjectured by Gross in 1988. A dual calculation can also be performed and equivalent results are obtained by taking the high-energy limit of Virasoro constraints. Finally, we compute all high-energy scattering amplitudes of three tachyons and one massive state at the leading order by saddle-point approximation to verify our results.     

Hidden symmetries in two dimensional field theory

The bosonization process elegantly shows the equivalence of massless scalar and fermion fields in two space-time dimensions. However, with multiple fermions the technique often obscures global symmetries. Witten’s non-Abelian bosonization makes these symmetries explicit, but at the expense of a somewhat complicated bosonic action. Frenkel and Kac have presented an intricate mathematical formalism relating the various approaches. Here, I reduce these arguments to the simplest case of a single massless scalar field. In particular, using only elementary quantum field theory concepts, I expose a hidden SU (2) × SU (2) chiral symmetry in this trivial theory. I then discuss in what sense this field should be interpreted as a Goldstone boson.