{A} Higher Spin Gravity in five dimensions is constructed. It was shown recently that constructing formally consistent classical equations of motion of higher spin gravities is equivalent to finding a certain deformation of a given higher spin algebra. A strong homotopy algebra encoding the interaction vertices then follows. We propose two different and novel realizations of the deformed higher spin algebra in the case of five dimensions: one in terms of the universal enveloping algebra of $su(2,2)$ and the other by means of oscillator variables. Both the new realizations admit supersymmetric extensions and the $\mathcal{N}=8$ case underlies the massless sector of tensionless strings.
Rotating IIB strings in AdS_5 x S^5 become ultra-relativistic, and hence effectively tensionless, in the limit of large angular momentum on S^5. We have shown previously that such tensionless strings may preserve supersymmetry. Here we extend this result to include a class of supersymmetric tensionless strings with arbitrary SO(6) angular momentum. We close with some general comments on tensionless strings in AdS_5 x S^5.
The covariant quantization of the tensionless free bosonic (open and closed) strings in AdS spaces is obtained. This is done by representing the AdS space as an hyperboloid in a flat auxiliary space and by studying the resulting string constrained hamiltonian system in the tensionless limit. It turns out that the constraint algebra simplifies in the tensionless case in such a way that the closed BRST quantization can be formulated and the theory admits then an explicit covariant quantization scheme. This holds for any value of the dimension of the AdS space.
We study the physical Fock space of the tensionless string theory with perimeter action which has pure massless spectrum. The states are classified by the Wigner's little group for massless particles. The ground state contains infinite many massless fields of fixed helicity, the excitation levels realize CSR representations. We demonstrate that the first and the second excitation levels are physical null states.
We discuss the notion of tensionless limit in quantum bosonic string theory, especially in flat Minkowski space, noncompact group manifolds (e.g., SL(2,R)) and coset manifolds (e.g., AdS). We show that in curved space typically there exists a critical value of the tension which is related to the critical value of the level of the corresponding affine algebra. We argue that at the critical level the sring theory becomes tensionless and that there exists a huge new symmetry of the theory. We dicuss the appearence of the higher spin massless states at the critical level.
We consider closed free tensionless strings in $AdS_d$, calculate exactly the boundary/boundary string evolution kernel and find the string dynamics to be completely frozen. We interpret therefore the boundary configurations as Wilson loop operators in a confining phase. This is taken as an argument in favor to the dual weakly coupled abelian gauge theory being that of $(d-4)$-forms in the $(d-1)$ dimensional boundary Minkowski space.
It is shown that a class of rotating strings in AdS_5 x S^5 with SO(6) angular momenta (J,J',J') preserve 1/8-supersymmetry for large J,J', in which limit they are effectively tensionless; when J=0, supersymmetry is enhanced to 1/4. These results imply that recent checks of the AdS/CFT correspondence actually test a nearly-BPS sector.
Consequences of a strong version of the AdS/CFT correspondence for extremely stringy physics are examined. In particular, properties of N = 4 supersymmetric Yang-Mills theory are used to extract results about interacting tensionless strings and massless higher spin fields in an AdS_5 x S^5 background. Furthermore, the thermodynamics of this model signals the presence of a Hawking-Page phase transition between AdS_5 space and a "black hole"-like high temperature configuration even in the extreme string limit.
The tensionless string theory with perimeter action has pure massless spectrum of higher-spin gauge fields. The multiplicity of these massless states grows linearly. It is therefore much less compared with the standard string theory and is larger compared with the field theory models of the Yang-Mills type. It is important to define nontrivial interaction between infinite amount of massless particles of the perimeter string theory. The appropriate vertex operators were defined recently and I study the lowest order vertex operators and the corresponding scattering amplitudes in tree approximati…
We report on progress in formulating a field theory of tensionless strings in $AdS_3$, starting from the dual large-$N$ symmetric orbifold CFT. We propose a set of field equations which are gauge invariant under the higher spin algebra of the theory, the `Higher Spin Square'. The massless higher spin sector is captured by a Chern-Simons gauge field, while the matter sector is described by unfolded equations similar to those appearing in Vasiliev theory. Our equations incorporate the full perturbative spectrum of the theory, including states coming from the twisted sectors, and capture some of …
It was recently shown in arXiv:2009.11306 that tree-level correlation functions in tensionless string theory on $\rm{AdS}_3\times\rm{S}^3\times\mathbb{T}^4$ match the expected form of correlation functions in the symmetric orbifold CFT on $\mathbb{T}^4$ in the large $N$ limit. This analysis utilized the free-field realization of the $\mathfrak{psu}(1,1|2)_1$ Wess-Zumino-Witten model, along with a surprising identity directly relating these correlation functions to a branched covering of the boundary of $\rm{AdS}_3$. In particular, this identity implied the unusual feature that the string theor…
The spectrum of superstrings on ${\rm AdS}_3 \times {\rm S}^3 \times \mathbb{M}_4$ with pure NS-NS flux is analysed for the background where the radius of the AdS space takes the minimal value $(k=1)$. Both for $\mathbb{M}_4={\rm S}^3 \times {\rm S}^1$ and $\mathbb{M}_4 = \mathbb{T}^4$ we show that there is a special set of physical states, coming from the bottom of the spectrally flowed continuous representations, which agree in precise detail with the single particle spectrum of a free symmetric product orbifold. For the case of ${\rm AdS}_3 \times {\rm S}^3 \times \mathbb{T}^4$ this relies …
We review old and recent results on a special limit of string theory on AdS$_3\times M_7$ with pure NS-NS fluxes: the limit in which the string length $\ell_s=\sqrt{α'}$ equals the AdS$_3$ radius $R $. At this point of the moduli space, the theory exhibits special properties, which we discuss. Special attention is focused on features of correlation functions that are related to the non-compactness of the boundary CFT target space, and on how these features change when the point $k\equiv R^2/α' =1$ is approached. Also, we briefly review recent proposals for exact realizations of AdS/CFT corresp…
We find various supersymmetric configurations of toroidal M2 brane solutions in $\AdS_4 \times S^7$ or, more generally, in $\AdS_4 \times S^7/Z_k$. In this class we identify solutions preserving 1/4 and 1/8 supersymmetries of the background. The supersymmetric M2 branes have angular momenta and winding on $S^7$, and null world-volumes. In certain cases they collapse to string-like configurations. These configurations can be viewed as a higher-dimensional (membrane) analog of BMN states. We compute the energy and angular momenta, showing that all supersymmetric configurations obey the BPS relat…
We describe a supersymmetric example of the holographic duality between 3 dimensional vector models and higher spin gauge theories in AdS_4, first proposed in a bosonic context by Klebanov and Polyakov. We argue that a particular Fradkin-Vasiliev type supersymmetric higher spin gauge theory in AdS_4 with 16 supersymmetries is dual to the singlet sector of bilinear operators of a free N = 4, SU(N) vector model defined on the boundary. Starting from the duality between type IIB on AdS_5 \times S^5 with a D5-brane as an AdS_4 \times S^2 subspace and the 4 dimensional SU(N) SYM with a defect, we r…
A classical action is proposed which upon quantisation yields massless particles belonging to the continuous spin representation of the Poincaré group. The string generalisation of the action is identical to the tensionless extrinsic curvature action proposed by Savvidy. We show that the BRST quantisation of the string action gives a critical dimension of 28. The constraints result in a number of degrees of freedom which is the same as the bosonic string.
I study the physical Fock space of the tensionless string theory with perimeter action, exploring its new gauge symmetry algebra. The cancellation of conformal anomaly requires the space-time to be 13-dimensional. All particles are massless and there are no tachyon states in the spectrum. The zero mode conformal operator defines the levels of the physical Fock space. All levels can be classified by the highest Casimir operator W of the little group E(11) for massless particles in 11-dimensions. The ground state is infinitely degenerated and contains massless gauge fields of arbitrary large int…
We consider string theory on $\text{AdS}_3 \times \text{S}^3 \times \mathbb{T}^4$ in the tensionless limit, with one unit of NS-NS flux. This theory is conjectured to describe the symmetric product orbifold CFT. We consider the string on different Euclidean backgrounds such as thermal $\text{AdS}_3$, the BTZ black hole, conical defects and wormhole geometries. In simple examples we compute the full string partition function. We find it to be independent of the precise bulk geometry, but only dependent on the geometry of the conformal boundary. For example, the string partition function on ther…
Considering the zero 't Hooft coupling limit of ${\cal N}=4$ super-Yang-Mills theory, the exact spectrum of all single-trace operators can be accessed in terms of the underlying $so(2,4)$ character. This makes it possible in turn to compute the one-loop free energy of the tensionless type IIB string theory in AdS$_5\times$S$^5$ background, with help of the recently developed method of character integral representation of zeta function (CIRZ). We calculate first the one-loop free energy of the string states in the $(p-1)$-th Regge trajectory and find the result to be $p$ times the free energy o…
In this thesis, two aspects of string theory are discussed, tensionless strings and supersymmetric sigma models. The equivalent to a massless particle in string theory is a tensionless string. Even almost 30 years after it was first mentioned, it is still quite poorly understood. We discuss how tensionless strings give rise to exact solutions to supergravity and solve closed tensionless string theory in the ten dimensional maximally supersymmetric plane wave background, a contraction of AdS(5)xS(5) where tensionless strings are of great interest due to their proposed relation to higher spin ga…
We investigate the behaviour of the bosonic string on AdS3 with H-flux at stringy scales, looking in particular for a `tensionless' limit in which there are massless higher spin gauge fields. We do this by revisiting the physical spectrum of the sl(2,R)$_k$ WZW model and considering the limit in which k becomes small. At k=3 we find that there is an infinite stringy tower of massless higher spin fields which are part of a continuum of light states. This can be viewed as a novel tensionless limit, which appears to be distinct from that inferred from the symmetric orbifold description of superst…
In the tensionless limit of string theory on flat background all the massive tower of states gets squeezed to a common zero mass level and the free theory is described by an infinite amount of massless free fields with arbitrary integer high spin. We notice that in this situation the very notion of critical dimension gets lost, the apparency of infinite global symmetries takes place, and the closed tensionless string can be realized as a constrained subsystem of the open one in a natural way. Moreover, we study the tensionless limit of the Witten's cubic sting field theory and find that the th…
String theory with perimeter action is tensionless by its geometrical nature and has pure massless spectrum of higher spin gauge particles. I demonstrate that liner transformation of the world-sheet fields defines a map to the SO(D,D) sigma model equipped by additional Abelian constraint, which breaks SO(D,D) to a diagonal SO(1,D-1). The effective tension is equal to the square of the dimensional coupling constant of the perimeter action. This correspondence allows to view the perimeter action as a "square root" of the Nambu-Goto area action. The aforementioned map between tensionless strings …
T-duality is used to extract information on an instanton of zero size in the $E_8\times E_8$ heterotic string. We discuss the possibility of the appearance of a tensionless anti-self-dual non-critical string through an implementation of the mechanism suggested by Strominger of two coincident 5-branes. It is argued that when an instanton shrinks to zero size a tensionless non-critical string appears at the core of the instanton. It is further conjectured that appearance of tensionless strings in the spectrum leads to new phase transitions in six dimensions in much the same way as massless parti…
We find an intriguing link between the symmetries of the tensionless limit of closed string theory and the 2-dimensional Galilean Conformal Algebra (2d GCA). 2d GCA has been discussed in the context of the non-relativistic limit of AdS/CFT and more recently in flat-space holography as the proposed symmetry algebra of the field theory dual to 3d Minkowski spacetimes. It is best understood as a contraction of two copies of the Virasoro algebra. In this note, we link this to the tensionless limit of bosonic closed string theory. We show how it emerges naturally as a contraction of the residual ga…
We test various conjectures about quantum gravity for six-dimensional string compactifications in the framework of F-theory. Starting with a gauge theory coupled to gravity, we analyze the limit in Kähler moduli space where the gauge coupling tends to zero while gravity is kept dynamical. We show that such a limit must be located at infinite distance in the moduli space. As expected, the low-energy effective theory breaks down in this limit due to a tower of charged particles becoming massless. These are the excitations of an asymptotically tensionless string, which is shown to coincide with a…
We argue for the existence of phase transitions in $3+1$ dimensions associated with the appearance of tensionless strings. The massless spectrum of this theory does not contain a graviton: it consists of one $N=2$ vector multiplet and one linear multiplet, in agreement with the light-cone analysis of the Green-Schwarz string in $3+1$ dimensions. In M-theory the string decoupled from gravity arises when two 5-branes intersect over a three-dimensional hyperplane. The two 5-branes may be connected by a 2-brane, whose boundary becomes a tensionless string with $N=2$ supersymmetry in $3+1$ dimensio…
We construct an off-shell extension of cubic interaction vertices between massless bosonic Higher Spin fields on a flat background which can be obtained from perturbative bosonic string theory. We demonstrate how to construct higher quartic interaction vertices using a simple particular example. We examine whether BCFW recursion relations for interacting Higher Spin theories are applicable. We argue that for several interesting examples such relations should exist, but consistency of the theories might require that we supplement Higher Spin field theories with extended and possibly non-local o…
We discuss the singularities in the moduli space of string compactifications to six dimensions with $N=1$ supersymmetry. Such singularities arise from either massless particles or non-critical tensionless strings. The points with tensionless strings are sometimes phase transition points between different phases of the theory. These results appear to connect all known $N=1$ supersymmetric six-dimensional vacua.
Massless spinning particle and tensionless string models on $AdS_d$ background in the projective-space realization are proposed as constrained Hamiltonian systems. Various forms of particle and string Lagrangians are derived and classical mechanics is studied including the Lax-type representation of the equations of motion. After that transition to the quantum theory is discussed. Analysis of potential anomalies in the tensionless string model necessitates introduction of ghosts and BRST charge. It is shown that quantum BRST charge is nilpotent for any $d$ if coordinate-momentum ordering for t…
We consider N=2 superconformal theories defined on a 3+1 dimensional hyperplane intersection of two sets of M5 branes. These theories have (tensionless) BPS string solitons. We use a dual supergravity formulation to deduce some of their properties via the AdS/CFT correspondence.
We study a string theory which is exclusively based on extrinsic curvature action. It is a tensionless string theory because the action reduces to perimeter for the flat Wilson loop. We are able to solve and quantize this high-derivative nonlinear two-dimensional conformal field theory. The absence of conformal anomaly in quantum theory requires that the space-time should be 13-dimensional. We have found that all particles, with arbitrary large spin, are massless. This pure massless spectrum is consistent with the tensionless character of the theory and we speculate that it may describe unbrok…
In this paper we study a simple gravity model dual to a (2+1)-dimensional system with a boundary at finite charge density and temperature. In our naive AdS/BCFT extension of a well known AdS/CFT system a non-zero charge density must be supported by a magnetic field. As a result, the Hall conductivity is a constant inversely proportional to the coefficients of pertinent topological terms. Since the direct conductivity vanishes, such behaviors resemble that of a quantum Hall system with Fermi energy in the gap between the Landau levels. We further analyze the properties stemming from our hologra…
In this note, we briefly introduce singleton representations and discuss their relevance to the study of string and brane configurations in AdS space, their tensionless limit and the connection with higher-spin gauge theory. We then discuss the main properties of subcritical SO(D-1,2) WZW models featuring singletons and their composites as primary fields. After a suitable gauging, these models are good candidates for a fundamental, partonic description of tensionless branes in AdS. Their massless sector provides an affine Lie-algebraic setting for the study of higher-spin symmetries. Based on …
We continue our study of the worldsheet theory of superstrings on $\mathrm{AdS}_3 \times \mathrm{S}^3 \times \mathbb{T}^4$ in the tensionless limit arXiv:1911.00378. We consider the theory on higher genus surfaces. We give evidence that the worldsheet correlators localise on certain worldsheets that cover the boundary of $\mathrm{AdS}_3$ holomorphically. This simplifies the string moduli space integral dramatically to a finite sum. This property shows that the higher genus corrections of the string worldsheet reproduce the structure of the $1/N$ corrections in the dual symmetric orbifold CFT $…
Massless fields of generic Young symmetry type in $AdS_d$ space are analyzed. It is demonstrated that in contrast to massless fields in Minkowski space whose physical degrees of freedom transform in irreps of $o(d-2)$ algebra, $AdS$ massless mixed symmetry fields reduce to a number of irreps of $o(d-2)$ algebra. From the field theory perspective this means that not every massless field in flat space admits a deformation to $AdS_d$ with the same number of degrees of freedom, because it is impossible to keep all of the flat space gauge symmetries unbroken in the AdS space. An equivalent statemen…
In the framework of light-cone formulation of relativistic dynamics, arbitrary spin massless fields propagating in the four-dimensional AdS space are studied. For such fields, the complete list of light-cone gauge cubic interaction vertices is obtained. Realization of relativistic symmetries on space of light-cone gauge massless AdS fields is also obtained. The light-cone gauge vertices for massless AdS fields take simple form similar to the one for massless fields in the flat space.
We consider a perturbation of the Einstein gravity with the Neumann boundary condition, which is regarded as an end of the world brane (ETW brane) of the AdS/BCFT correspondence, in the AdSd+1 spaectime where d is larger than 2. We obtain the mode expansion of the perturbations explicitly for the tensionless ETW brane case. We also show that the energy-momentum tensor in a d-dimensional BCFT should satisfy nontrivial constraints other than the ones for the boundary conformal symmetry if the BCFT can couple to a d-dimensional gravity with a specific boundary condition, which can be the Neumann …
Lax representation is elaborated for the equations of motion of massless superparticle on the AdS_4 x CP^3 superbackground that proves their classical integrability.
We solve the Dirichlet boundary value problem for the massless gravitino on $AdS_{d+1}$ space and compute the two-point function of the dual CFT supersymmetry currents using the $AdS$/CFT correspondence principle. We find analogously to the spinor case that the boundary data for the massless $(d+1)$ dimensional bulk gravitino field consists of only a $(d-1)$ dimensional gravitino.
Free arbitrary spin massless and self-dual massive fields propagating in $AdS_5$ are investigated. We study totally symmetric and mixed symmetry fields on an equal footing. Light-cone gauge action for such fields is constructed. As an example of application of light-cone formalism we discuss $AdS/CFT$ correspondence for massless arbitrary spin $AdS$ fields and corresponding boundary operators at the level of two point function.
We generalize the ideas and formalism of Two-Time Physics from particle dynamics to some specific examples of string and p-brane (p >= 1) dynamics. The two-time string or p-brane action can be gauge fixed to produce various one-time string or p-brane actions that are dual to each other under gauge transformations. We discuss the particular gauges that correspond to tensionless strings and p-branes in flat (d-1)+1 spacetime, rigid strings and p-branes in flat (d-1)+1 spacetime, and tensionless strings and p-branes propagating in the AdS_{d-n} x S^n backgrounds.
Particular class of AdS(d) mixed-symmetry bosonic massless fields corresponding to arbitrary two-column Young tableaux is considered. Unique gauge invariant free actions are found and equations of motion are analyzed.
It is natural to believe that the free symmetric product orbifold CFT is dual to the tensionless limit of string theory on AdS3 x S3 x T4. At this point in moduli space, string theory is expected to contain a Vasiliev higher spin theory as a subsector. We confirm this picture explicitly by showing that the large level limit of the N=4 cosets of arXiv:1305.4181, that are dual to a higher spin theory on AdS3, indeed describe a closed subsector of the symmetric product orbifold. Furthermore, we reorganise the full partition function of the symmetric product orbifold in terms of representations of…
We study massless and massive Hawking radiations on a two-dimensional AdS spacetime. For the massless case, the quantum stress-energy tensor of a massless scalar field on the AdS background is calculated, and the expected null radiation is obtained. However, for the massive case, the scattering analysis is performed in order to calculate the absorption and reflection coefficients which are related to statistical Hawking temperature. On the contrary to the massless case, we obtain a nonvanishing massive radiation.
We study a 3d/2d dimensional degression which is a Kaluza-Klein type mechanism in AdS$_3$ space foliated into AdS$_2$ hypersurfaces. It is shown that an AdS$_3$ massless particle of spin $s=1,2,...,\infty$ degresses into a couple of AdS$_2$ particles of equal energies $E=s$. Note that the Kaluza-Klein spectra in higher dimensions are always infinite. To formulate the AdS$_3$/AdS$_2$ degression we consider branching rules for AdS$_3$ isometry algebra o$(2,2)$ representations decomposed with respect to AdS$_2$ isometry algebra o$(1,2)$. We find that a given o$(2,2)$ higher-spin representation ly…
The string equivalent of a massless particle ($m=0$) is the tensionless string ($T=0$). The study of such strings is of interest when trying to understand the high energy limit of ordinary strings. I discuss the classical $T\to 0$ limit of the bosonic string, the spinning string and the superstring. A common feature is the appearence of a space-time (super-)conformal symmetry replacing the world-sheet Weyl invariance. The question of whether this symmetry may survive quantization is addressed. A lightcone analysis of the quantized bosonic tensionless string leads to severe constraints on the p…
Free AdS(5) mixed-symmetry massless bosonic and fermionic gauge fields of arbitrary spins are described by using su(2,2) spinor language. Manifestly covariant action functionals are constructed and field equations are derived.
Generic solution of free equations for massless fields of an arbitrary spin in $AdS_4$ is built in terms of the star-product algebra with spinor generating elements. A class of "plane wave" solutions is described explicitly.
Using BRST-BV formulation of relativistic dynamics, arbitrary spin massless and massive field propagating in flat space and arbitrary spin massless fields propagating in AdS space are considered. For such fields, BRST-BV Lagrangians invariant under gauge transformations are obtained. The Lagrangians and gauge transformations are built in terms of traceless gauge fields and traceless gauge transformation parameters. The use of the Poincare parametrization of AdS space allows us to get simple BRST-BV Lagrangian for AdS fields. By imposing the Siegel gauge condition, we get gauge-fixed Lagrangian…
