We reinvestigate the kappa-symmetry-fixed Green-Schwarz action in the AdS_5 x S^5 background in a version of the light-cone gauge. In the generalized light-cone gauge, the action has been written in the phase space variables. We convert it into the standard action written in terms of the fields and their derivatives. We obtain a Nambu-Goto type action which has the correct flat-space limit.
We calculate, using zeta function regularization method, semiclassical energy of the Nambu-Goto string supplemented with the boundary, Gauss-Bonnet term in the action and discuss the tachyonic ground state problem.
We show that the measure of the three dimensional Nambu-Goto string theory has a simple decomposition as a measure on two parameter group of induced area-preserving transformations of the immersed surface and a trivial measure for the area of the surface.
We show how Weyl degrees of freedom, can be introduced in the Nambu-Goto string in the path integral formulation using reparametrization invariant measure. We first identify Weyl degrees in conformal gauge using BFV formulation. Further we change Nambu-Goto string action to Polyakov action. The generating functional in light-cone gauge is then obtained from the generating func- tional corresponding to Polyakov action in conformal gauge by using suitably constructed finite field dependent BRST transformation.
We examine the relativistic Nambu-Goto model with Gauss-Bonnet boundary term added to the action integral. The system is analysed using an invariant representation of dynamical string degrees of freedom by complex Liouville fields. The solutions of classical equations of motion for open strings are described.
We present news path integral studies on the Polyakov Non-Critical and Nambu-Goto critical string theories and its applications to QCD SU((infinity)) interquark potential .
It is shown that the critical (or deconfinement) temperature for the Nambu-Goto string connecting the point-like masses (quarks) does not depend on the value of these masses. This temperature turns out to be the same as that in the case of string with fixed ends (infinitely heavy immobile quarks).
We organize the eight variables of the four-dimensional bosonic string ({\dot X}^μ, X'^μ) into a 2 x 2 x 2 hypermatrix a_{AA'A''} and show that in signature (2,2) the Nambu-Goto Lagrangian is given by \sqrt{Det a} where Det is Cayley's hyperdeterminant. This is invariant not only under [SL(2,R)]^{3} but also under interchange of the indices A, A' and A''. This triality reveals hitherto hidden discrete symmetries of the Nambu-Goto action.
For the $σ$-model and Nambu-Goto actions, values of the Alday-Maldacena-regularized actions are calculated on solutions of the equations of motion with constant non-regularized Lagrangian. It turns out that these values coincide up to a factor, independent of boundary conditions.
We extend a recent analysis of gravitational perturbations on Dirac-Nambu-Goto strings, membranes and higher dimensional branes. In an arbitrary gauge, it is shown that the relevant first order equations governing the displacement vector of the worldsheet and metric perturbation are obtainable from a variational principle whose Lagrangian is constructed as a second order perturbation of the standard Dirac-Goto-Nambu action density. A symplectic current functional is obtained as a by-product that is potentially useful for the derivation of conservation laws in particular circumstances.
We assume the bosonic string is a composite object of the relativistic particles. The behavior of the relativistic particles in a curve enables us to obtain the Nambu-Goto and the Polyakov actions of the bosonic string. We observe that the particles of these strings move with non-constant speeds along them.
We calculate (using zeta function regularization) the Casimir energy of the rotating Nambu-Goto string with the Gauss-Bonnet term in the action and point-like masses at the ends. The resulting value turns out to be negative for all values of the parameters of the model.
The classical linearised gravitational self interaction of a Goto-Nambu string is examined in four spacetime dimensions. Using a conveniently gauge independent tensorial treatment, the divergent part of the self-force is shown to be exactly zero. This is due to cancelation by a contribution that was neglected in the previous treatments. This result has implications for many applications.
We establish explicitely the relation between the algebraic and Nambu-Goto strings when the target space is a four dimensional flat space. We find that the two theories are exactly equivalent only when the algebraic string is restricted to the self-dual or anti self-dual sectors. In its Hamiltonian formulation, the algebraic string defines a constrained system with first and second class constraints. In the self-dual case, we exhibit the appropriate set of second class constraints such that the resulting physical phase space is formulated in the same way as it is in the standard Nambu-Goto str…
We examine and implement the concept of non-additive composition laws in the quantum theory of closed bosonic strings moving in (3+1)-dimensional Minkowski space. Such laws supply exact selection rules for the merging and splitting of closed strings.
Using a fully covariant formalism given by Carter for the deformation dynamics of p-branes governed by the Dirac-Nambu-Goto action in a curved background, it is proved that the corresponding Witten's phase space is endowed with a covariant symplectic structure, which can serve as a starting point for a phase space quantization of such objects. Some open questions for further research are outlined.
The presentation of the algebra of classical observables of the closed bosonic Nambu-Goto-String in 3+1 dimensions is given for the massless case $P^2=0,P\neq0$ in the relevant standard frame up to and including the second stratum. The elements and the relations of this algebra established so far are presented in the form of irreducible multiplets of the stabilizer group $E_2$ of the light-like vector $P$ in its standard form.
The spectrum of quenched Yang-Mills theory in the large-N limit displays strings and higher dimensional extended objects. The effective dynamics of string-like excitations is encoded into area preserving Schild action. In this letter, we bridge the gap between SU(N) gauge models and fully reparametrization invariant Nambu-Goto string models by introducing an extra matrix degree of freedom in the Yang-Mills action. In the large-N limit this matrix variable becomes the world-sheet auxiliary field allowing a smooth transition between the Schild and Nambu-Goto strings. The new improved matrix mode…
The reduced covariant phase space associated with the three-dimensional Euclidean Nambu-Goto action can be identified, via the Enneper-Weierstrass representation of minimal surfaces, with the space of complex analytic functions plus three translational zero modes. The symplectic structure induced trough the Enneper-Weierstrass map can be explicitly computed. Quantization is then straightforward, yielding as a result a target-space Euclidean-invariant, positive-definite, two-dimensional quantum field theory. The physical states are shown to correspond with particles states of integer spin and a…
I consider higher-order terms of the Seeley expansion of the heat kernel, which for smooth metrics are suppressed as inverse powers of the UV cutoff $Λ$, and demonstrate how they result in an anomalous contribution to the string effective action after doing uncertainties $Λ^{-2}\times Λ^2$. For the Polyakov string these anomalies precisely reproduce at one loop the result of KPZ-DDK obtained for the Liouville theory by the conformal field theory technique. For the Nambu-Goto string I find a deviation from this result which shows that the two string formulations may differ.
We explore the formation of cosmic string Y-junctions when strings of two different types collide, which has recently become important since string theory can yield cosmic strings of distinct types. Using a model containing two types of local U(1) string and stable composites, we simulate the collision of two straight strings and investigate whether the dynamics matches that previously obtained using the Nambu-Goto action, which is not strictly valid close to the junction. We find that the Nambu-Goto action performs only moderately well at predicting when the collision results in the formation…
In this article I describe my own stumblings in the first string era. This was a time when most of the active people were very young, not very knowledgeable and the field was completely new. Many of us had little training for what we came to work on, and it took quite some time to accomplish the new conceptual discoveries.
A relevant part of the quantum algebra of observables for the closed bosonic strings moving in 1+3-dimensional Minkowski space is presented in the form of generating relations involving still one, as yet undetermined, real free parameter.
In this paper we solve the non-linear Lagrange's equations for the Nambu-Goto closed bosonic string. We show that Ultradistributions of Exponential Type (UET) are appropriate for the description in a consistent way string and string field theories. We also prove that the string field is a linear superposition of UET of compact support (CUET), and give the notion of anti-string. We evaluate the propagator for the string field, and calculate the convolution of two of them.
The quantum algebra of observables postulated in hep-th/9805057 is constructed up to degree five. All independent relations of degree four are given; they involve three as yet undetermined parameters. Definitions and symbols are used as introduced in the above-mentioned article.
We investigate classical strings defined by the Nambu-Goto action with the boundary term added. We demonstrate that the latter term has a significant bearing on the string dynamics. It is confirmed that new action terms that depend on higher order derivatives of string coordinates cannot be considered as continuous perturbations from the starting string functional. In the case the boundary term reduces to the Gauss-Bonnet term, a stability analysis is performed on the rotating rigid string solution. We determined the most generic solution that the fluctuations grow to. Longitudinal string exci…
Gravitational field of a cylindrical Nambu-Goto wall in the vacuum spacetime is considered in order to clarify the interaction between Nambu-Goto membranes and gravitational waves. If one neglects the emission of gravitational waves by the wall motion, the spacetime becomes singular. It is also shown that the emission of gravitational waves does occur by the motion of the cylindrical wall if the initial data is singularity free. The energy loss rate due to radiation of gravitational waves agrees with that estimated from the test wall motion and the quadrupole formula for the gravitational wave…
We initiate the study of multiloop scattering amplitudes in the Nambu-Goto theory on the worldsheet of a non-critical string. We start with a brute force calculation of two loop four particle scattering. Somewhat surprisingly, even though non-trivial UV counterterms are present at this order, on-shell amplitudes remain polynomial in the momenta of colliding particles. We show that this can be understood as a consequence of existence of certain close by (semi)integrable models. Furthermore, these arguments can be extended to obtain the answer for three and four loop scattering, bypassing the br…
We consider the QCD string as an effective string, whose action describes long-range stringy fluctuations. The leading infrared contribution to the ground state energy is given by the Alvarez-Arvis formula, usually derived using the Nambu-Goto action. Here we rederive it by a saddle point calculation using the Polyakov formulation of the free string, where the world sheet metric and the target space coordinates are treated as independent variables. The next order relevant in the infrared term in the effective action is the extrinsic curvature term. We show that the spectrum does not change ord…
It has been recently shown that Nambu-Goto action can be re-expressed in terms of Cayley's hyperdeterminant with the manifest SL(2,R) X SL(2,R) X SL(2,R) symmetry. In the present paper, we show that the same feature is shared by Green-Schwarz sigma-model for N=2 superstring whose target space-time is D=2+2. When its zweibein field is eliminated from the action, it contains the Nambu-Goto action which is nothing but the square root of Cayley's hyperdeterminant of the pull-back in superspace \sqrt{\hyperdet(Π_{i \a\Dot\a})} manifestly invariant under SL(2,R) X SL(2,R) X SL(2,R). The target space…
We compute the string susceptibility $γ_{str}$ for the regularized Nambu-Goto string in $d$ dimensions and obtain $γ_{str}=1/2 $ in $2<d<26$. This agrees with previous results obtained for lattice strings.
We propose a novel prescription to take off the square root of Nambu-Goto action for a p-brane, which generalizes the Brink-Di Vecchia-Howe-Tucker or also known as Polyakov method. With an arbitrary decomposition as d+n=p+1, our resulting action is a modified d-dimensional Polyakov action which is gauged and possesses a Nambu n-bracket squared potential. We first spell out how the (p+1)-dimensional diffeomorphism is realized in the lower dimensional action. Then we discuss a possible gauge fixing of it to a direct product of $d$-dimensional diffeomorphism and n-dimensional volume preserving di…
We show that a Nambu-Goto string has a nontrivial zero length limit which corresponds to a massless particle with extrinsic curvature. The system has the set of six first class constraints, which restrict the phase space variables so that the spin vanishes. Upon quantization, we obtain six conditions on the state, which can be represented as a wave function of position coordinates, $x^μ$, and velocities, $q^μ$. We have found a wave function $ψ(x,q)$ that turns out to be a general solution of the corresponding system of six differential equations, if the dimensionality of spacetime is eight. Th…
We consider a bosonic string propagating in 4--dim Minkowski space. We show that in the orthonormal gauge the classical system exhibits a hidden $W_{\infty}$ chiral symmetry, arising from the equivalence of its transverse modes with the $SU(2)/U(1)$ coset model defined on the string world--sheet. Generalizations to other string backgrounds are proposed. We also define a Liouville--like transformation that maps solutions of the $SU(2)/U(1)$ coset model into the solution space of two decoupled Liouville theories. Inverting this transformation, however, remains an open problem.
It is shown that all Polchinski-Strominger effective string theories are \emph{isospectral} to Nambu-Goto theory. The relevance of these results to QCD-Strings is discussed.
Recently, a new quantization method for gauge theories was proposed, in which no gauge fixing is required but the constraints are kept. Here we successfully applied this formalism to Nambu-Goto action in any dimensions. The result of our theoretical calculation have shown striking agreement with the spectrum of the light-quark mesons.
We present solutions of the Nambu-Goto equation for test strings in a shape of toroidal spiral in five-dimensional spacetimes. In particular, we show that stationary toroidal spirals exist around the five-dimensional Myers-Perry black holes. We also show the existence of innermost stationary toroidal spirals around the five-dimensional black holes like geodesic particles orbiting around four-dimensional black holes.
In the present paper we investigate classical dynamics of the Nambu-Goto string with the Gauss-Bonnet term in the action and point-like masses at the ends in the context of effective QCD string. The configurations of rigidly rotating string is studied and its application to phenomenological description of meson is discussed.
It is shown that the algebra of diffeomorphism-invariant charges of the Nambu-Goto string cannot be quantized in the framework of canonical quantization. The argument is shown to be independent of the dimension of the underlying Minkowski space.
We propose a method to obtain new exact solutions of spinning p-branes in flat space-times for any p, which manifest themselves as higher dimensional Euler Tops and minimize their energy functional. We provide concrete examples for the case of spherical topology S^{2}, S^{3} and rotational symmetry \prod_{i}SO(q_{i}). In the case of toroidal topology T^{2}, T^{3} the rotational symmetry is \prod SU(q_{i}) and m target dimensions are compactified on the torus T^{m} . By double dimensional reduction the Light Cone Hamiltonians of T^{2}, T^{3} reduce to those of closed string S^{1} and T^{2} memb…
We compute semi-classical corrections to the energy of rotating closed Nambu-Goto strings. We confirm the results obtained by means of the Polchinski-Strominger action. We also show that in this semi-classical approximation, the spectrum of physical excitations contains modes that are unphysical non-perturbatively, i.e., to which no physical excitations of the covariantly quantized Nambu-Goto string correspond.
The hitherto controversial proposition that a ``wiggly" Goto-Nambu cosmic string can be effectively represented by an elastic string model of exactly transonic type (with energy density $U$ inversely proportional to its tension $T$) is shown to have a firm mathematical basis.
A four dimensional Superstring is constructed starting from a twenty six dimensional bosonic string. Fermions are introduced by noting the Manselstam's proof of equivalence of two fermions to one boson in 1+1 dimensions. The action of the superstring is invariant under SO(6)$\times$ SO(5). It has four bosonic coordinates and twenty four Majorana fermions of SO(3,1) representing two transverse modes of super fermions and conformal ghosts (b,c). The super conformal ghosts ($β, γ$) are the quanta of an extended Hilbert space of the remaining longitudinal modes of two superfermions. The massless s…
We compute semi-classical corrections to the energy of rotating open Nambu-Goto strings with and without masses at the ends, using methods from quantum field theory on curved space-times.
The Batalin-Vilkovisky data for Polyakov string theory on a manifold with (non-null) boundary is shown to induce compatible Batalin--Fradkin--Vilkovisky data, thus allowing BV-quantisation on manifolds with boundary. On the other hand, the analogous formulation of Nambu--Goto string theory fails to satisfy the needed regularity requirements. As a byproduct, a concise description is given of the reduced phase spaces of both models and their relation, for any target $d$-dimensional Lorentzian manifold.
We discuss a way to evaluate the full prediction for the interquark potential which is expected from the effective Nambu-Goto string model. We check the correctness of the prescription reproducing the results obtained with the zeta function regularization for the first two perturbative orders. We compare the predictions with existing Monte Carlo data for the (2+1) dimensional Z(2), SU(2) and SU(3) gauge theories: in the low temperature regime, we find good agreement for large enough interquark distances, but an increasing mismatch between theoretical predictions and numerical results is observ…
The theory of the usual, constrained p-branes is embedded into a larger theory in which there is no constraints. In the latter theory the Fock-Schwinger proper time formalism is extended from point-particles to membranes of arbitrary dimension. For this purpose the tensor calculus in the infinite dimensional membrane space M is developed and an action which is covariant under reparametrizations in M is proposed. The canonical and Hamiltonian formalism is elaborated in detail. The quantization appears to be straightforward and elegant. No problem with unitarity arises. The conventional p-brane …
We propose a simple effective model for the description of interfaces in 2d statistical models, based on the first-order treatment of an action corresponding to the length of the interface. The universal prediction of this model for the interface free energy agrees with the result of an exact calculation in the case of the 2d Ising model. This model appears as a dimensional reduction of the Nambu-Goto stringy description of interfaces in 3d, i.e., of the capillary wave model.
Motivated by the recent progress in the effective string description of the interquark potential in lattice gauge theory, we study interfaces with periodic boundary conditions in the three-dimensional Ising model. Our Monte Carlo results for the associated free energy are compared with the next-to-leading order (NLO) approximation of the Nambu-Goto string model. We find clear evidence for the validity of the effective string model at the level of the NLO truncation.
We study the perturbative dynamics of an infinite gravitating Nambu-Goto string within the general-relativistic perturbation framework. We develop the gauge invariant metric perturbation on a spacetime containing a self-gravitating straight string with a finite thickness and solve the linearized Einstein equation. In the thin string case, we show that the string does not emit gravitational waves by its free oscillation in the first order with respect to its oscillation amplitude, nevertheless the string actually bends when the incidental gravitational waves go through it.
Thickness corrections to static, axisymmetric Dirac-Nambu-Goto branes embedded into spherically symmetric black hole spacetimes with arbitrary number of dimensions are studied. First, by applying a perturbative approximation, it is found that the thick solutions deviate significantly in their analytic properties from the thin ones near the axis of the system, and perturbative approaches around the thin configurations can not provide regular thick solutions above a certain dimension. For the general case, a non-perturbative, numerical approach is applied and regular solutions are obtained for a…
In this work, we study the computational complexity of massive gravity theory via the "Complexity = Action" conjecture. Our system contains a particle moving on the boundary of the black hole spacetime. It is dual to inserting a fundamental string in the bulk background. Then this string would contribute a Nambu-Goto term, such that the total action is composed of the Einstein-Hilbert term, Nambu-Goto term and the boundary term. We shall investigate the time development of this system, and mainly discuss the features of the Nambu-Goto term affected by the graviton mass and the horizon curvatur…
We study the self-similar motion of a string in a self-similar spacetime by introducing the concept of a self-similar string, which is defined as the world sheet to which a homothetic vector field is tangent. It is shown that in Nambu-Goto theory, the equations of motion for a self-similar string reduce to those for a particle. Moreover, under certain conditions such as the hypersurface orthogonality of the homothetic vector field, the equations of motion for a self-similar string simplify to the geodesic equations on a (pseudo) Riemannian space. As a concrete example, we investigate a self-si…
We consider a covariant approach to coarse-graining a network of interacting Nambu-Goto strings. A transport equation is constructed for a spatially flat Friedmann universe. In Minkowski space and with no spatial dependence this model agrees with a previous model. Thus it likewise converges to an equilibrium with a factorizability property. We present an argument that this property does not depend on a `string chaos' assumption on the correlations between strings. And in contrast to the earlier model, this transport equation agrees with conservation equations for a fluid of strings derived fro…
We study the evolution of non-periodic cosmic string loops containing Y-junctions, such as may form during the evolution of a network of (p,q) cosmic superstrings. We set up and solve the Nambu-Goto equations of motion for a loop with junctions, focusing attention on a specific static and planar initial loop configuration. After a given time, the junctions collide and the Nambu-Goto description breaks down. We also study the same loop configuration in a U(1)xU(1) field theory model that allows composite vortices with corresponding Y-junctions. We show that the field theory and Nambu-Goto evolu…
We study the effect of a probe string to black hole complexity according to the CA (Complexity equals Action) conjecture. Our system contains a particle moving on the boundary of black hole spacetime. In the dual description this corresponds to the insertion of a fundamental string on the bulk spacetime. The total action consists of the Einstein-Hilbert term and the Nambu-Goto term. The effect of this string is expressed by the Nambu-Goto term. Focusing on the Nambu-Goto term, we analyse the time development of this system. Our results show some interesting properties of complexity. This gives…
The effective action on long strings, such as confining strings in pure Yang-Mills theories, is well-approximated by the Nambu-Goto action, but this action cannot be exact. The leading possible corrections to this action (in a long string expansion in the static gauge), allowed by Lorentz invariance, were recently identified, both for closed strings and for open strings. In this paper we compute explicitly in a Hamiltonian formalism the leading corrections to the lowest-lying Nambu-Goto energy levels in both cases, and verify that they are consistent with the previously computed effective stri…
