Nambu-Goto Term Research Articles

Pacman geometries and the Hayward term in JT gravity

We study the Hayward term describing corners in the boundary of the geometry in the context of the Jackiw-Teitelboim gravity. These corners naturally arise in the computation of Hartle-Hawking wave functionals and reduced density matrices, and give origin to AdS spacetimes with conical defects.This set up constitutes a lab to manifestly realize many aspects of the construction recently proposed in [1]. In particular, it can be shown that the Hayward term is required to reproduce the flat spectrum of Rényi entropies in the Fursaev’s derivation, and furthermore, the action with an extra Nambu-Goto term associated to the Dong’s cosmic brane prescription appears naturally.On the other hand, the conical defect coming from Hayward term contribution are subtly different from the defects set as pointlike sources studied previously in the literature. We study and analyze these quantitative differences in the path integral and compare the results. Also study previous proposals on the superselection sectors, and by computing the density operator we obtain the Shannon entropy and some novel results on the symmetry group representations and edge modes. It also makes contact with the so-called defect operator found in [2].Lastly, we obtain the area operator as part of the gravitational modular Hamiltonian, in agreement with the Jafferis-Lewkowycz-Maldacena-Suh proposal.

Rotating black hole with a probe string in Horndeski gravity

In this work, we present the effect of a probe string on the complexity of a black hole according to the CA (Complexity equals action) conjecture on Horndeski's gravity. In our system, we consider a particle moving on the boundary of black hole spacetime in ($2+1$)-dimensions. To obtain a dual description, we need to insertion a fundamental string on the bulk spacetime. The effect of this string is given by the Nambu-Goto term. For the Nambu-Goto term, we can analyze the time development of this system, which is affected by the parameters of Horndeski's gravity. In our case, we show some interesting complexity properties for this gravity.

Complexity growth of rotating black holes with a probe string

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 a useful hint for defining complexity in quantum field theories.

Supersymmetric coupling of a self-dual string to a (2,0) tensor multiplet background

We construct an interaction between a (2,0) tensor multiplet in six dimensions and a self-dual string. The interaction is a sum of a Nambu-Goto term, with the tension of the string given by the modulus of the scalar fields of the tensor multiplet, and a non-local Wess-Zumino term, that encodes the electromagnetic coupling of the string to the two-form gauge field of the tensor multiplet. The interaction is invariant under global (2,0) supersymmetry, modulo the equations of motion of a free tensor multiplet. It is also invariant under a local fermionic kappa-symmetry, as required by the BPS-property of the string.

SU(N) confining strings

String representations of the Wilson loop are constructed in the SU(N)-version of compact QED in three and four dimensions. This is done exactly in the case of the fundamental Wilson loop and in the large-N limit in the case of the adjoint Wilson loop. Using for concreteness the three-dimensional fundamental case, it is demonstrated how the resulting SU(N)-generalization of the so-called theory of confining strings can be obtained in various ways. In its weak-field limit (corresponding to the limit of low monopole densities), this theory enables one to fix the value of the string tension, which cannot be fixed when deduced from the mean magnetic field inside a flat contour (the derivation of this field is also presented). Moreover, the obtained theory enables one to find also the coupling constants of terms in the expansion of the nonlocal string effective action, which are higher in the derivatives than the Nambu-Goto term (some of these terms vanish at the flat surface). In the four-dimensional case with the theta-term, the critical values of the theta-parameter, at which the problem of crumpling of large world sheets might be solved, are found in both the fundamental case and in the large-N limit of the adjoint case. These values are only accessible provided the electric coupling constant is larger than a certain value, in accordance with the known fact that confinement in the four-dimensional compact QED holds in the strong-coupling regime.

Universality in effective strings

We demonstrate that, due to the finite thickness of domain walls, and the consequent ambiguity in defining their locations, the effective string description obtained by integrating out bulk degrees of freedom contains ambiguities in the coefficients of the various geometric terms. The only term with unambiguous coefficient is the zeroth order Nambu-Goto term. We argue that fermionic ghost fields which implement gauge-fixing act to balance these ambiguities. The renormalized string tension, obtained after integrating out both bulk and world-sheet degrees of freedom, can be defined in a scheme independent manner; and we compute the explicit finite expressions, to one-loop, for the case of compact quantum electrodynamics and phi-4 theory.

NONPERTURBATIVE FIELD CORRELATOR AND STRING REPRESENTATION FOR THE 't HOOFT LOOP AVERAGE IN THE ABELIAN HIGGS MODEL

Making use of the duality transformation, we derive in the Londons' limit of the Abelian Higgs model string representation for the 't Hooft loop average defined on the string worldsheet, which yields the values of two coefficient functions parametrizing the bilocal correlator of the dual field strength tensors. The asymptotic behaviors of these functions agree with the ones obtained within the method of vacuum correlators in QCD in the lowest order of perturbation theory. We demonstrate that the bilocal approximation to the method of vacuum correlators is an exact result in the Londons' limit, i.e. all the higher cumulants in this limit vanish. We also show that at large distances, apart from the integration over metrics, the obtained string effective theory (which in this case reduces to the nonlinear massive axionic sigma model) coincides with the low energy limit of the dual version of 4D compact QED, the so-called universal confining string theory. We derive string tension of the Nambu–Goto term and the coupling constant of the rigidity term for the obtained string effective theory and demonstrate that the latter is always negative, which means the stability of strings, while the positiveness of the former is confirmed by the present lattice data. These data enable us to find the Higgs boson charge and the vacuum expectation value of the Higgs field, which well-described QCD. We also study dynamics of the weight factor of the obtained string representation for the 't Hooft average in the loop space. In conclusion, we obtain string representation for the partition function of the correlators of an arbitrary number of Higgs currents, by virtue of which we rederive the structure of the bilocal correlator of the dual field strength tensors, which yields the surface term in the string effective action.

Curvature Expansion for the Gluodynamics String Including Perturbative Gluonic Contributions

Perturbation theory, which represents a Wilson loop in the SU(2) gluodynamics as an integral over all the orientations in color space, in the nonperturbative QCD vacuum and the non-Abelian Stokes theorem is applied to a derivation of the correction to the string effective action in the lowest order in the coupling constant g. This correction is due to the interaction of perturbative gluons with the string worldsheet and affects only the coupling constant of the rigidity term, while its contribution to the string tension of the Nambu–Goto term vanishes. The obtained correction to the rigidity coupling constant multiplicatively depends on the color "spin" of the representation of the Wilson loop under consideration and a certain path integral, which includes the background Wilson loop average.

Curvature expansion for the background-induced gluodynamics string

Abstract Using the cumulant expansion for an averaged Wilson loop we derive an action of the gluodynamics string in the form of a series in powers of the correlation length of the vacuum. In the lowest orders it contains the Nambu-Goto term and the rigidity term with corresponding coupling constants computed from the bilocal correlator of gluonic fields.

CURVATURE EXPANSION FOR THE BACKGROUND-INDUCED GLUODYNAMICS STRING

Using the cumulant expansion for an averaged Wilson loop we derive an action of the gluodynamics string in the form of a series in powers of the correlation length of the vacuum. In the lowest orders it contains the Nambu–Goto term and the rigidity term with the corresponding coupling constants computed from the bilocal correlator of gluonic fields. Some higher derivative corrections are also calculated.

Topological rigid string theory and two-dimensional QCD

We present a string theory that reproduces the large-N expansion of two-dimensional Yang-Mills gauge theory on arbitrary surfaces. First, a new class of topological sigma models is introduced, with path integrals localized to the moduli space of harmonic maps. The Lagrangian of these harmonic topological sigma models is of fourth order in worldsheet derivatives. Then we gauge worldsheet diffeomorphisms by introducing the induced worldsheet metric. This leads to a topological string theory, whose Lagrangian coincides in the bose sector with the rigid string Lagrangian discussed some time ago by Polyakov and others as a candidate for QCD string theory. The path integral of this topological rigid string theory is localized to the moduli spaces of minimal-area maps, and calculates their Euler numbers. The dependence of the large- N QCD partition functions on the target area emerges from measuring the volume of the moduli spaces, and can be reproduced by adding a Nambu-Goto term (improved by fermionic terms) to the Lagrangian of the topological rigid string.

Classical dynamics of the rigid string from the Willmore functional

A new approach for investigating the classical dynamics of the relativistic string model with rigidity is proposed. It is based on the embedding of the string world surface into a space of constant curvature. It is shown that the rigid string in flat space-time is described by the Euler-Lagrange equation for the Willmore functional in a space-time of constant curvature K = − γ/(2 α), where γ and α are constants in front of the Nambu-Goto term and the curvature term in the rigid string action, respectively. For simplicity the Euclidean version of the rigid string in three-dimensional space-time is considered. The Willmore functional (the action for the “Willmore string”) is obtained by dropping the Nambu-Goto term in the Polyakov-Kleinert action for the rigid string. Such a “reduction” of the rigid string model would be useful, for example, by applying some results about the Nambu-Goto string dynamics in the de Sitter universe to the rigid string model in the Minkowski space-time. It also allows us to use numerous mathematical results about Willmore surfaces in the context of the physical problem.

“Topological” formulation of effective vortex strings

We present a “topological” formulation of arbitrarily shaped vortex strings in four dimensional field theory. By using a large Higgs mass expansion, we then evaluate the effective action of the closed Abrikosov-Nielsen-Olesen vortex string. It is shown that the effective action contains the Nambu-Goto term and an extrinsic curvature squared term with negative sign. We next evaluate the topological F μνF̃ μν term in the case where the vortex string manifold extends out to the boundary of the time direction of space-time and find that it becomes the sum of an ordinary self-intersection number and Polyakov's self-intersection number of the world sheet swept by the vortex string. These self-intersection numbers are related to the self-linking number and the total twist number, respectively. Furthermore, the F μνF̃ μν term turns out to be the difference between the sum of the writhing numbers and the linking numbers of the vortex strings at the initial time and the one at the final time. When the vortex string is coupled to fermions, the chiral fermion number of the vortex string becomes the writhing number (modulo Z) through the chiral anomaly. Our formulation is also applied to “global” vortex strings in a model with a broken global U(1) symmetry.

RENORMALIZATION OF COUPLINGS IN EMBEDDED RANDOM SURFACES

We study the dressing of operators and flows of corresponding couplings in models of embedded random surfaces. We show that these dressings can be obtained by applying the methods of David and Distler and Kawai. We consider two extreme limits. In the first limit the string tension is large and the dynamics is dominated by the Nambu-Goto term. We analyze this theory around a classical solution in the situation where the length scale of the solution is large compared to the length scale set by the string tension. Couplings get dressed by the Liouville mode (which is now a composite field) in a non-trivial fashion. However this does not imply that the excitations around a physical “long string” have a phase space corresponding to an extra dimension. In the second limit the string tension is small and the dynamics is governed by the extrinsic curvature term. We show, perturbatively, that in this theory the relationship between the induced metric and the worldsheet metric is “renormalized,” while the extrinsic curvature term receives a non-trivial dressing as well. This has the consequence that in a generic situation the dependence of couplings on the physical scale is different from that predicted by their beta functions.

Fine structure of local and axion strings.

We examine the nature of the internal structure of strings arising from field theories when a global or local symmetry is spontaneously broken. The classical dynamics of these strings is represented by effective Lagrangians in which the standard Nambu-Goto term is supplemented by additional terms that are geometric in nature. In the simplest case of the local string, the new term is just the extrinsic curvature of the world sheet. For the axion string, terms of the same order as the extrinsic curvature must be added involving the coupling of the axion to the curvature itself.

Phase transitions in random surfaces

We investigate the statistical properties of triangulated random surfaces of fixed connectivity embedded in d-dimensional space and weighted with an action that contains the extrinsic curvature of the surface as well as the usual Nambu-Goto term. Numerically, we find no second-order phase transition for finite values of the rigidity coupling, in contrast to results obtained by Kantor and Nelson using a different action. Rather, there is a third order “crumpling” transition which, however, is not associated with an infinite correlation length between the normals to the surface. We compare the Monte Carlo results with several approximations, particularly with the mean field solution of the model. Our results indicate that there are no fixed points other than those already found in perturbation theory. We comment on several other aspects of random surfaces.

Glueballs from spontaneous strings.

I point out that in Euclidean space spontaneous strings (equivalentstrings with extrinsic curvature stiffness and spontaneously generated tension) can form glueballs, even at the classical level (in contrast with the ordinary string). In the limit of infinite dimensions, the fluctuations can be integrated out and the glueballs are found to have a mass to tension ratio of approx. =3.5 in the purely spontaneous case (equivalentno Nambu-Goto tension term in the action).

Adorning the string action

The string action is considered which contains, in addition to the standard Nambu-Goto term, a scale invarient term. The integration of this model yields the σ-model of a null vector in Minkowski space.

Fine structure of strings

We show that the critical behavior of the string tension and most other important qualitative properties of strings are driven by a term in the action containing extrinsic curvatures, which is necessary to add to the Nambu-Goto term. Depending on the renormalization-group structure, strings can be “creased” (with non-zero surface tension at the critical point) or “smooth”. Candidates for both possibilities and their physical relevance are discussed.