Goto String Research Articles

Opus on conformal symmetry of the Nambu–Goto versus Polyakov strings

I investigate the Nambu–Goto and Polyakov strings, accounting for higher-derivative terms in the emergent action for the metric tensor which are classically negligible for smooth metrics but revive quantumly. Using the conformal field theory technique by KPZ-DDK, I compute in the one-loop approximation the conformal dimension and the central charge which differs in the two cases, telling the Nambu–Goto and Polyakov strings apart. I confirm the results by explicit quantum field theory computations of the propagator and the energy–momentum tensor at one loop, using the Pauli–Villars regularization.

Thermodynamics of 4D dS/AdS Gauss–Bonnet black holes according to consistent gravity theory in the presence of a cloud of strings

By looking at the Lovelock theorem one can infer that the gravity model given by [1] cannot be applicable for all types of 4D Einstein–Gauss–Bonnet (EGB) curved space-time. The reason for this is that in 4D space-time, the Gauss–Bonnet invariant is a total derivative and hence it does not contribute to gravitational dynamics. Hence, the authors of [2] presented an alternative consistent EGB gravity model instead of [1] by applying a break-of-diffeomorphism property. In this work, we use the alternative model to produce a de Sitter (dS)/Anti-de Sitter (AdS) black hole metric and then investigate its thermodynamic behavior in the presence of a cloud of Nambu–Goto strings. Mathematical derivations show that the resulting diagrams of pressure vs specific volume at a constant temperature are similar to that for a van der Waals gas/fluid in an ordinary thermodynamic system in the dS sector but not in the AdS background. From this, we infer that the black hole participates in the small-to-large black hole phase transition in the dS background, while it exhibits a Hawking–Page phase transition in the AdS background. In the latter case, an evaporating black hole eventually reaches an AdS vacuum space because of its instability.

The susceptibility exponent of Nambu–Goto strings

We compute the string susceptibility [Formula: see text] for the regularized Nambu–Goto string in [Formula: see text] dimensions and obtain [Formula: see text] in [Formula: see text]. This agrees with previous results obtained for lattice strings.

Revisiting the flux tube spectrum of 3d SU(2) lattice gauge theory

We perform a high-precision measurement of the spectrum of the flux tube in three-dimensional {text {SU}}(2) gauge theory at multiple lattice spacings. We compare the results at large qbar{q} separations R to the spectrum predicted by the effective string theory, including the leading-order boundary term with a nonuniversal coefficient. We find qualitative agreement with the predictions from the leading-order Nambu–Goto string theory down to small values of R, while, at the same time, observing the predicted splitting of the second excited state due to the boundary term. On fine lattices and at large R, we observe slight deviations from the EST predictions for the first excited state.

Complete integrability of cohomogeneity-one strings in Rn,1 and canonical form of Killing vector algebra

The equation of motion for cohomogeneity-one Nambu–Goto strings in flat space Rn,1 has been investigated. We first classify possible forms of the Killing vector fields in Rn,1 after appropriate action of the Poincaré group. Then, all possible forms of the Hamiltonian for the cohomogeneity-one Nambu–Goto strings are determined. It has been shown that the system always has the maximum number of functionally independent, pair-wise commuting conserved quantities, i.e., it is completely integrable. We have also determined all the possible coordinate forms of the Killing vector basis for the two-dimensional noncommutative Lie algebra.

Information theoretic bounds on cosmic string detection in CMB maps with noise

ABSTRACT We use a convolutional neural network to study cosmic string detection in cosmic microwave background (CMB) flat sky maps with Nambu–Goto strings. On noiseless maps, we can measure string tensions down to order 10−9, however when noise is included we are unable to measure string tensions below 10−7. Motivated by this impasse, we derive an information theoretic bound on the detection of the cosmic string tension Gμ from CMB maps. In particular, we bound the information entropy of the posterior distribution of Gμ in terms of the resolution, noise level and total survey area of the CMB map. We evaluate these bounds for the ACT, SPT-3G, Simons Observatory, Cosmic Origins Explorer, and CMB-S4 experiments. These bounds cannot be saturated by any method.

Rigidly rotating string sticking in a Kerr black hole

We analyze rigidly rotating Nambu--Goto strings in the Kerr spacetime, particularly focusing on the strings sticking in the horizon. From the regularity on the horizon, we find the condition for sticking in the horizon, which is consistent with the second law of the black hole thermodynamics. Energy extraction through the sticking string from a Kerr black hole occurs. We obtain the maximum value of the luminosity of the energy extraction.

Studies on Polyakov and Nambu–Goto random surface path integrals on QCD(SU(∞)): Interquark potential and phenomenological scattering amplitudes

We present new path integral studies on the Polyakov noncritical and Nambu–Goto critical string theories and their applications to [Formula: see text] interquark potential. We also evaluate the long distance asymptotic behavior of the interquark potential on the Nambu–Goto string theory with an extrinsic term in Polyakov’s string at [Formula: see text]. We also propose an alternative and a new view to covariant Polyakov’s string path integral with a fourth-order two-dimensional quantum gravity, is an effective stringy description for [Formula: see text] at the deep infrared region.

Predicting cusps or kinks in Nambu–Goto dynamics

It is known that Nambu–Goto extended objects present some pathological structures, such as cusps and kinks, during their evolution. In this paper, we propose a model through the generalized Raychaudhuri (Rh) equation for membranes to determine if there are cusps and kinks in the worldsheet. We extend the generalized Rh equation for membranes to allow the study of the effect of higher order curvature terms in the action on the issue of cusps and kinks, using it as a tool for determining when a Nambu–Goto string generates cusps or kinks in its evolution. Furthermore, we present three examples where we test graphically this approach.

Point Particle with Extrinsic Curvature as a Boundary of a Nambu–Goto String: Classical and Quantum Model

It is shown how a string living in a higher dimensional space can be approximated as a point particle with squared extrinsic curvature. We consider a generalized Howe–Tucker action for such a “rigid particle” and consider its classical equations of motion and constraints. We find that the algebra of the Dirac brackets between the dynamical variables associated with velocity and acceleration contains the spin tensor. After quantization, the corresponding operators can be represented by the Dirac matrices, projected onto the hypersurface that is orthogonal to the direction of momentum. A condition for the consistency of such a representation is that the states must satisfy the Dirac equation with a suitable effective mass. The Pauli–Lubanski vector composed with such projected Dirac matrices is equal to the Pauli–Lubanski vector composed with the usual, non projected, Dirac matrices, and its eigenvalues thus correspond to spin one half states.

A non-trivial zero length limit of the Nambu–Goto string

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, xμ, and velocities, qμ. 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. Although classically the system is just a point particle with vanishing extrinsic curvature and spin, the quantized system is not trivial, because it is consistent in eight, but not in arbitrary, dimensions.

Observational constraints on the types of cosmic strings

This paper is aimed at setting observational limits to the number of cosmic strings (Nambu–Goto, Abelian-Higgs, semilocal) and other topological defects (textures). Radio maps of CMB anisotropy, provided by the space mission Planck for various frequencies, were filtered and then processed by the method of convolution with modified Haar functions (MHF) to search for cosmic string candidates. This method was designed to search for solitary strings, without additional assumptions as regards the presence of networks of such objects. The sensitivity of the MHF method is $$\delta T \approx 10~\upmu \hbox {K}$$ in a background of $$\delta T \approx 100~\upmu \hbox {K}$$ . The comparison of these with previously known results on search string network shows that strings can only be semilocal in the range of $$1 \div 5$$ , with the upper restriction on individual string tension (linear density) of $$G\mu /c^2 \le 7.36 \times 10^{-7}$$ . The texture model is also legal. There are no strings with $$G\mu /c^2 > 7.36 \times 10^{-7}$$ . However, a comparison with the data for the search of non-Gaussian signals shows that the presence of several (up to three) Nambu–Goto strings is also possible. For $$G\mu /c^2 \le 4.83 \times 10^{-7}$$ the MHF method is ineffective because of unverifiable spurious string candidates. Thus the existence of strings with tensions $$G\mu /c^2 \le 4.83 \times 10^{-7}$$ is not prohibited but it is beyond the Planck data possibilities. The same string candidates have been found in the WMAP 9-year data. Independence of Planck and WMAP data sets serves as an additional argument to consider those string candidates as very promising. However, the final proof should be given by optical deep surveys.

Three dimensional finite temperature [formula omitted] gauge theory near the phase transition

We have measured the correlation function of Polyakov loops on the lattice in three dimensional SU(3) gauge theory near its finite temperature phase transition. Using a new and powerful application of finite size scaling, we furthermore extend the measurements of the critical couplings to considerably larger values of the lattice sizes, both in the temperature and space directions, than was investigated earlier in this theory. With the help of these measurements we perform a detailed finite size scaling analysis, showing that for the critical exponents of the two dimensional three state Potts model the mass and the susceptibility fall on unique scaling curves. This strongly supports the expectation that the gauge theory is in the same universality class. The Nambu–Goto string model on the other hand predicts that the exponent ν has the mean field value, which is quite different from the value in the abovementioned Potts model. Using our values of the critical couplings we also determine the continuum limit of the value of the critical temperature in terms of the square root of the zero temperature string tension. This value is very near to the prediction of the Nambu–Goto string model in spite of the different critical behaviour.

Isgur–Wise function for heavy–light mesons in the D-dimensional potential model

We report the results of a wave function for mesons in D space–time dimension developed by considering the quark–antiquark potential of Nambu–Goto strings. With this wave function, we have studied the Isgur–Wise function for heavy–light mesons and its derivatives such as slope and curvature. The dimensional dependence of our results and a comparative study with the results of three-dimensional QCD are also reported.

Can holography reproduce the QCD Wilson line?

Recently a remarkable agreement was found between lattice simulations of long Wilson lines and behavior of the Nambu Goto string in flat space-time. However, the latter fails to fit the short distance behavior since it admits a tachyonic mode for a string shorter than a critical length. In this paper we examine the question of whether a classical holographic Wilson line can reproduce the lattice results for Wilson lines of any length. We determine the condition on the the gravitational background to admit a Coulombic potential at short distances. We analyze the system using three different renormalization schemes. We perform an explicit best fit comparison of the lattice results with the holographic models based on near extremal D3 and D4 branes, non-critical near extremal AdS6 model and the Klebanov Strassler model. We find that all the holographic models examined admit after renormalization a constant term in the potential. We argue that the curves of the lattice simulation also have such a constant term and we discuss its physical interpretation.

JACOBI FIELDS IN GEODESIC SURFACE CONGRUENCES

Using the Nambu–Goto string action in the space of the surfaces spanned by closed strings in a spacetime manifold, we investigated the geodesic surface equation in the space of surfaces joining two given strings and the geodesic surface deviation equation in geodesic surface congruence which yields a Jacobi field along a given geodesic surface, and singularities in geodesic surface congruences. In this paper, assuming that the singularity exists in geodesic surface congruences in a conformally symmetric manifold, we compute the Jacobi fields of the geodesic surface deviation equations and observe them.

OPEN STRING IN (3+1)-DIMENSIONAL REISSNER–NORDSTRÖM BLACK HOLE

Previously we investigated the Nambu–Goto string and the wiggly cosmic string in (3+1)-dimensional Schwarzschild black hole. As an extension the solutions in (3+1)-dimensional spherically symmetric charged black holes are investigated. The solution for the wiggly string exhibits open strings lying along the circular orbit in the equatorial plane outside horizon, while the Nambu–Goto string has only a point-like solution.

Exactly solvable strings in Minkowski spacetime

We study the integrability of the equations of motion for the Nambu–Goto strings with a cohomogeneity-one symmetry in Minkowski spacetime. A cohomogeneity-one string has a world surface which is tangent to a Killing vector field. By virtue of the Killing vector, the equations of motion reduce to the geodesic equation in the orbit space. Cohomogeneity-one strings are classified into seven classes (types I to VII). We investigate the integrability of the geodesic equations for all the classes and find that the geodesic equations are integrable. For types I to VI, the integrability comes from the existence of Killing vectors on the orbit space which are the projections of Killing vectors on Minkowski spacetime. For type VII, the integrability is related to a projected Killing vector and a nontrivial Killing tensor on the orbit space. We also find that the geodesic equations of all types are exactly solvable, and show the solutions.

Evolution and stability of cosmic string loops with Y-junctions

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 evolution are remarkably similar until the collision time. However, in the field theory evolution a new phenomenon occurs: the composite vortices can unzip, producing in the process new Y-junctions, whose separation may grow significantly, destabilizing the configuration. In particular, an initial loop with two Y-junctions may evolve to a configuration with six Y-junctions (all distant from each other). Setting up this new configuration as an initial condition for Nambu Goto strings, we solve for its evolution and establish conditions under which it is stable to the decay mode seen in the field theory case. Remarkably, the condition closely matches that seen in the field theory simulations, and is expressed in terms of simple parameters of the Nambu-Goto system. This implies that there is an easy way to understand the instability in terms of which region of parameter space leads to stable or unstable unzippings.

Conformal SO(2, 4) transformations of the one-cusp Wilson loop surface

By applying the conformal SO(2, 4) transformations to the elementary one-cusp Wilson loop surface we construct various two-cusp and four-cusp Wilson loop surface configurations in AdS5 and demonstrate that they solve the string equations of the Nambu–Goto string action. The conformal boosts of the basic four-cusp Wilson loop surface with a square-form projection generate various four-cusp Wilson loop surfaces with projections of the rescaled square, the rhombus and the trapezium, on which surfaces the classical Euclidean Nambu–Goto string actions in the IR dimensional regularization are evaluated.