Effective String Research Articles

The Unreasonable effectiveness of effective string theory: The case of the 3D SU(2) Higgs model

We study string breaking in the three dimensional SU(2) Higgs model, using values of the gauge coupling for which the confinement-like and Higgs-like regions of the phase diagram are separated just by a smooth crossover. We show that even in the presence of string breaking, the confining part of the interquark potential is well described by the Effective String Theory and that also the fine details of the effective string, like the higher order terms of the Nambu-Goto action or the boundary correction, can be precisely extracted from the fits and agree with the effective string predictions. We comment on the implications of these results for QCD simulations with dynamical quarks.

3D Yang-Mills glueballs vs closed effective strings

Recent lattice results strongly support the Axionic String Ansatz (ASA) for quantum numbers of glueballs in 3D Yang-Mills theory. The ASA treats glueballs as closed bosonic strings. The corresponding worldsheet theory is a deformation of the minimal Nambu-Goto theory. In order to understand better the ASA strings and as a first step towards a perturbative calculation of the glueball mass splittings we compare the ASA spectrum to the closed effective string theory. Namely, we model glueballs as excitations around the folded rotating rod solution with a large angular momentum J. The resulting spectrum agrees with the ASA in the regime of validity of the effective theory, i.e., in the vicinity of the leading Regge trajectory. In particular, closed effective string theory correctly predicts that only glueballs of even spin J show up at the leading Regge trajectory. Interestingly though, the closed effective string theory overestimates the number of glueball states far above the leading Regge trajectory.

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.

Effective String Description of the Confining Flux Tube at Finite Temperature

In this review, after a general introduction to the Effective String Theory (EST) description of confinement in pure gauge theories, we discuss the behaviour of EST as the temperature is increased. We show that, as the deconfinement point is approached from below, several universal features of confining gauge theories, like the ratio Tc/σ0, the linear increase of the squared width of the flux tube with the interquark distance, or the temperature dependence of the interquark potential, can be accurately predicted by the effective string. Moreover, in the vicinity of the deconfinement point the EST behaviour turns out to be in good agreement with what was predicted by conformal invariance or by dimensional reduction, thus further supporting the validity of an EST approach to confinement.

Metric-connection geometries on pre-Leibniz algebroids: A search for geometrical structure in string models

Metric-affine and generalized geometries are arguably the appropriate mathematical frameworks for Einstein’s theory of gravity and low-energy effective string field theory, respectively. In fact, mathematical structures in a metric-affine geometry are constructed on the tangent bundle, which is itself a Lie algebroid, whereas those in generalized geometries, which form the basis of double field theories, are constructed on Courant algebroids. Lie, Courant, and higher Courant algebroids, which are used in exceptional field theories, are all known to be special cases of pre-Leibniz algebroids. As mathematical structures on these algebroids are essential in string models, it is natural to work on a more unifying geometrical framework. Provided with some additional ingredients, the construction of such geometries can all be carried over to regular pre-Leibniz algebroids. We define below the notions of locality structures and locality projectors, which are some necessary ingredients. In terms of these structures, E-metric-connection geometries are constructed with (possibly) a minimum number of assumptions. Certain small gaps in the literature are also filled as we go along. E-Koszul connections, as a generalization of Levi–Cività connections, are defined and shown to be helpful for some results including a simple generalization of the fundamental theorem of Riemannian geometry. The existence and non-existence of E-Levi–Cività connections are discussed for certain cases. We also show that metric-affine geometries can be constructed in a unique way as special cases of E-metric-connection geometries. Some aspects of Lie and Lie-type algebroids are studied, where the latter are defined here as a generalization of Lie algebroids. Moreover, generalized geometries are shown to follow as special cases, and various properties of linear generalized-connections are proven in the present framework. Similarly, uniqueness of the locality projector in the case of exact Courant algebroids is proven, a result that explains why the curvature operator, defined with a projector in the double field theory literature, is a necessity.

On the quantization of folded strings in non-critical dimensions

Classical rotating closed string are folded strings. At the folding points the scalar curvature associated with the induced metric diverges. As a consequence one cannot properly quantize the fluctuations around the classical solution since there is no complete set of normalizable eigenmodes. Furthermore in the non-critical effective string action of Polchinski and Strominger, there is a divergence associated with the folds. We overcome this obstacle by putting a massive particle at each folding point which can be used as a regulator. Using this method we compute the spectrum of quantum fluctuations around the rotating string and the intercept of the leading Regge trajectory. The results we find are that the intercepts are a = 1 and a = 2 for the open and closed string respectively, independent of the target space dimension. We argue that in generic theories with an effective string description, one can expect corrections from finite masses associated with either the endpoints of an open string or the folding points on a closed string. We compute explicitly the corrections in the presence of these masses.

Finite-size effects in the rough phase of the 3d Ising model

Using Monte Carlo simulations, finite-size effects of interfacial properties in the rough phase of the Ising on a cubic lattice with L×L×R sites are studied. In particular, magnetization profiles perpendicular to the flat interface of size L×R are studied, with L being considerably larger than R, in the (pre)critical temperature range. The resulting R-dependences are compared with predictions of the standard capillary-wave theory, in the Gaussian approximation, and with a field theory based on effective string actions, for L=∞.

Impact of single string structure and multiple string interaction on strangeness production in Pb+Pb collisions at sNN=2.76 TeV

We present a systematic study on the strange and multi-strange particles production in Pb+Pb collisions at $\sqrt{S_{NN}} = 2.76$ TeV based on the PACIAE model simulations. Two different mechanisms, namely the single string structure variations and multiple string interactions, are implemented in the simulations. These modifications give rise to an enhancement of the string tension value involved in the Lund string fragmentation framework and generate more strange particles in the hadronic final state. By comparing the simulation results with the ALICE experimental data, it turns out that the inclusion of the variable effective string tension in the PACIAE model is capable to reach an improved agreement between theory and experiment on the strangeness production in Pb+Pb collisions.

An Ultralow Complexity String Matching Approach to Screen Content Coding in AVS3

Screen content coding (SCC) is increasingly used in mobile devices, and ultralow coding complexity is required for low power consumption. This article proposes an ultralow complexity string matching approach to SCC. The proposed approach has two essential features: 1) allowing only two types of most effective reference strings that have two most frequently occurring values of offset (i.e., displacement vector) named dual unity offset and 2) fully optimized coding of string matching parameters for maximum coding efficiency. Since at most only two offset values and corresponding reference string positions are allowed for any current string being coded, the optimal reference string searching process is extremely simple and only needs to select the best string from at most two candidates. Moreover, in the proposed approach, the value ranges of string matching parameters, i.e., the string offset vector and string length are very limited, resulting in few bits to code the two parameters and high coding efficiency. Compared with the AVS3 reference software HPM7.0 with IBC disabled, using AVS3 SCC common test condition and YUV test sequences in text and graphics with motion category, the proposed technique achieves Y average BD-rate reduction of 10.8% and 5.8% for all intra (AI) and low-delay B (LDB) configurations, respectively, at ultralow encoding and decoding complexity.

Holographic Wilsonian renormalization of a heavy quark moving through a strongly coupled plasma

A heavy quark moving through a strongly coupled deconfined plasma has a holographic dual description as a string moving in a black brane geometry. We apply the holographic Wilsonian renormalization method to derive a holographic effective string action dual to the heavy quark. The effective action only depends on the geometry between the black brane horizon and a cutoff localized in the radial direction, corresponding to the IR of the dual theory. We derive RG flow equations for the coefficients in the effective action and show that the force acting on the heavy quark is independent of the position of the cutoff. All the information about the UV is hidden in integration constants of the RG flow equations. This type of approach could be used to improve semi-holographic models where the UV is described by perturbative QCD and the IR by a holographic model.

D→4 Einstein-Gauss-Bonnet gravity and beyond

A 'novel' pure theory of Einstein-Gauss-Bonnet gravity in four-spacetime dimensions can be constructed by rescaling the Gauss-Bonnet coupling constant, seemingly eluding Lovelock's theorem. Recently, however, the well-posedness of this model has been called into question. Here we apply a `dimensional regularization' technique, first used by Mann and Ross to write down a D→2 limit of general relativity, to the case of pure Einstein-Gauss-Bonnet gravity. The resulting four-dimensional action is a particular Horndeski theory of gravity matching the result found via a Kaluza-Klein reduction over a flat internal space. Some cosmological solutions of this four-dimensional theory are examined. We further adapt the technique to higher curvature Lovelock theories of gravity, as well as a low-energy effective string action with an α′ correction. With respect to the D→4 limit of the α′-corrected string action, we find we must also rescale the dilaton to have a non-singular action in four dimensions. Interestingly, when the conformal rescaling Φ is interpreted as another dilaton, the regularized string action appears to be a special case of a covariant multi-Galileon theory of gravity.

TT¯ deformation of the compactified boson and its interpretation in lattice gauge theory

We study the effective string description of space-like Polyakov loop correlators at finite temperature with the goal of describing the behaviour of the space--like string tension in the vicinity of the deconfinement transition. To this end we construct the partition function of the Nambu-Goto effective string theory in presence of a compact transverse direction of length $L$ equal to the inverse temperature. We then show that, under particular conditions, our result can be interpreted as the partition function of the $T\bar T$ deformation of the 2d quantum field theory describing a compactified bosonic field and that this mapping allows a deeper insight on the behaviour of the space-like observables of the theory. In particular we show, by imposing that the spectrum of the model obeys the inviscid Burgers equation, that the $T\bar T$ deformations follow well defined trajectories in the parameter space $(\sigma,L)$ of the model, where $\sigma$ is the string tension, which are characterized by a constant value of the dimensionless compactification radius $\rho=L\sqrt{\sigma/2\pi}$. We discuss the potential usefulness of these results for studying the space--like string tension of the underlying Lattice Gauge Theory and its behaviour across the deconfinement transition.

String breaking, baryons, medium, and gauge/string duality

We consider the string breaking phenomenon within effective string models which purport to mimic QCD with two light flavors, with a special attention to baryon modes. We make some estimates of the string breaking distances at zero and non-zero baryon chemical potentials. Our estimates point towards the enhancement of baryon production in strong decays of heavy mesons in dense baryonic matter. We also suggest that the enhanced production of $\Lambda_c^+$ baryons in PbPb collisions is mainly due to larger values of chemical potential.

Rotating black holes in cubic gravity

Using on-shell amplitude methods, we derive a rotating black hole solution in a generic theory of Einstein gravity with additional terms cubic in the Riemann tensor. We give an explicit expression for the metric in Einsteinian Cubic Gravity (ECG) and low energy effective string theory, which correctly reproduces the previously discovered solutions in the zero angular-momentum limit. We show that at first order in the coupling, the classical potential can be written to all orders in spin as a differential operator acting on the non-rotating potential, and we comment on the relation to the Janis-Newman algorithm. Furthermore, we derive the classical impulse and scattering angle for such a black hole and comment on the phenomenological interest of such quantities.

Baryon modes in string breaking from gauge/string duality

We consider the string breaking phenomenon within effective string models which purport to mimic QCD with two light flavors, with a special attention to baryon modes. We make some estimates of the string breaking distances at zero and non-zero baryon chemical potentials. Our estimates point towards the enhancement of baryon production in strong decays of heavy mesons in dense baryonic matter. We also suggest that the enhanced production of Λc+ baryons in PbPb collisions is mainly due to larger values of chemical potential.

Large-size expansion for triangular Wilson loops in confining gauge theories

The asymptotic behavior of Wilson loops in the large-size limit (L → ∞) in confining gauge theories with area law is controlled by effective string theory (EST). The L−2 term of the large-size expansion for the logarithm of Wilson loop appears within EST as a 2-loop correction. Ultraviolet divergences of this 2-loop correction for polygonal contours can be renormalized using an analytical regularization constructed in terms of Schwarz-Christoffel mapping. In the case of triangular Wilson loops this method leads to a simple final expression for the L−2 term.

On BPS World Volume, RR Couplings, and Their α′ Corrections in Type IIB

We compute the asymmetric and symmetric correlation functions of a four-point amplitude of a gauge field, a scalar field, and a closed string Ramond-Ramond (RR) for different nonvanishing BPS branes. All world volume, the Taylor and pull-back couplings, and their all-order α′ corrections have also been explored. Due to various symmetry structures, different restricted BPS Bianchi identities have also been constructed. The prescription of exploring all the corrections of two closed string RR couplings in type IIB is given. We obtain the closed form of the entire S-matrix elements of two closed string RRs and a gauge field on the world volume of BPS branes in type IIB. All the correlation functions of VA0x1VC−1z1,z¯1VC−1z2,z¯2 are also revealed accordingly. The algebraic forms for the most general case of the integrations ∫d2zz−iaz+ibz−z¯cz+z¯d on the upper half plane are derived in terms of Pochhammer and some analytic functions. Lastly, we generate various singularity structures in both effective field theory and IIB string theory, producing different contact interactions as well as their α′ higher derivative corrections.

Monte-Carlo study of long-range correlations of average transverse momentum and multiplicity for strange particles in pp-collisions at the LHC energies

This study is motivated by the puzzling enhanced production of multi-strange hadrons observed for the first time by the ALICE Collaboration in high-multiplicity pp-collisions at at the LHC. We investigate this effect of strangeness enhancement in pp-collisions in the framework of the MC event generator PYTHIA 8 where the collectivity processes are taken into account by the formation of a so-called flavour rope. The latter is hadronized with a larger effective string tension providing the increase of strangeness yield. This concept of the flavour rope, as a source of multi-strange hadrons, extended in rapidity, is being tested by the study of so called long-range correlations (LRC) between the average transverse momentum 〈pT〉 and multiplicity n for charged particles containing strange quarks produced in high energy pp-collisions.The dependencies of correlation coefficients bn−n, bPT−n and bPT−PT on the gap between forward and backward pseudorapidity windows, and on the width of the forward pseudorapidity windows, are studied and the results are discussed.

Tensionless Path from Closed to Open Strings.

We reconsider the tensionless limit on bosonic closed string theory, where the 3D Bondi-Metzner-Sachs (BMS) algebra appears as symmetries on the world sheet, as opposed to two copies of the Virasoro algebra in the case of the usual tensile theory. This is an ultrarelativistic limit on the world sheet. We consider the induced representations of the BMS algebra in the oscillator basis and show that the limit takes the tensile closed string vacuum to the "induced" vacuum, which is identified as a Neumann boundary state. Hence, rather remarkably, an open string emerges from closed strings in the tensionless limit. We also follow the perturbative states in the tensile theory in the limit and show that there is a Bose-Einstein-like condensation of all perturbative states on this induced vacuum. This ties up nicely with the picture of the formation of a long string from a gas of strings in the Hagedorn temperature, where the effective string tension goes to zero.

Exact effective interactions and 1/4-BPS dyons in heterotic CHL orbifolds

Motivated by precision counting of BPS black holes, we analyze six-derivative couplings in the low energy effective action of three-dimensional string vacua with 16 supercharges. Based on perturbative computations up to two-loop, supersymmetry and duality arguments, we conjecture that the exact coefficient of the \nabla^2(\nabla\phi)^4∇2(∇ϕ)4 effective interaction is given by a genus-two modular integral of a Siegel theta series for the non-perturbative Narain lattice times a specific meromorphic Siegel modular form. The latter is familiar from the Dijkgraaf-Verlinde-Verlinde (DVV) conjecture on exact degeneracies of 1/4-BPS dyons. We show that this Ansatz reproduces the known perturbative corrections at weak heterotic coupling, including tree-level, one- and two-loop corrections, plus non-perturbative effects of order e^{-1/g_3^2}e−1/g32. We also examine the weak coupling expansions in type I and type II string duals and find agreement with known perturbative results, . In the limit where a circle in the internal torus decompactifies, our Ansatz predicts the exact \nabla^2 F^4∇2F4 effective interaction in four-dimensional CHL string vacua, along with infinite series of exponentially suppressed corrections of order e^{-R}e−R from Euclideanized BPS black holes winding around the circle, and further suppressed corrections of order e^{-R^2}e−R2 from Taub-NUT instantons. We show that instanton corrections from 1/4-BPS black holes are precisely weighted by the BPS index predicted from the DVV formula, including the detailed moduli dependence. We also extract two-instanton corrections from pairs of 1/2-BPS black holes, demonstrating consistency with supersymmetry and wall-crossing, and estimate the size of instanton-anti-instanton contributions.