Linear Dilaton Research Articles

General continuum clockwork

The continuum clockwork is an extra-dimensional set-up to realize certain features of the clockwork mechanism generating exponentially suppressed or hierarchical couplings of light particles. We study the continuum clockwork in a general scheme in which large volume, warped geometry, and localization of zero modes in extra dimension are described by independent parameters. For this, we propose a generalized 5-dimensional linear dilaton model which can realize such set-up as a solution of the model, and examine the KK spectrum and the couplings of zero modes and massive KK modes to boundary-localized operators for the bulk graviton, Abelian gauge bosons and periodic scalar fields. We discuss how those KK spectra and couplings vary as a function of the volume, warping and localization parameters, and highlight the behavior in the parameter region corresponding to the clockwork limit. We discuss also the field range of 4-dimensional axions originating from either 5-dimensional periodic scalar field or the 5-th component of an Abelian gauge field, and comment on the limitations of continuum clockwork compared to the discrete clockwork.

Clockwork without supersymmetry

The clockwork mechanism would be completely spoiled by the presence of a cosmological constant in the bulk of its 5D construction, or by analogous terms in the discrete case. It is believed that supersymmetry is required to forbid the appearance of these fatal terms, thus apparently tying the fate of the clockwork to the presence of supersymmetry. In this letter we argue that a robust clockwork can be obtained also without supersymmetry, by providing a model for the clockwork/linear dilaton EFT where this protection is instead related to diffeomorphism invariance in a higher number of extra dimensions. We show that the clockwork mechanism is a quite general setup that emerges, rather minimally, from pure gravity in the presence of D−5 additional sufficiently flat extra dimensions. The linear dilaton model is obtained asymptotically in the limit of infinitely many extra dimensions. We then study the finite-D theory, which is a deformation of the linear dilaton one, but still a clockwork theory for D large enough.

Quantizing the rotating string with massive endpoints

We compute leading order quantum corrections to the Regge trajectory of a rotating string with massive endpoints using semiclassical methods. We expand the bosonic string action around a classical rotating solution to quadratic order in the fluctuations and perform the canonical quantization of the resulting theory. For a rotating string in D dimensions the intercept receives contributions from D − 3 transverse modes and one mode in the plane of rotation, in addition to a contribution due to the Polchinski-Strominger term of the non-critical effective string action when D ≠ 26. The intercept at leading order is proportional to the expectation value of the worldsheet Hamiltonian of the fluctuations, and this is shown explicitly in several cases. All contributions to the intercept are considered, and we show a simple physical method to renormalize the divergences in them. The intercept converges to known results at the massless limit, and corrections from the masses are explicitly calculated at the long string limit. In the process we also determine the quantum spectrum of the string with massive endpoints, and analyze the asymmetric case of two different endpoint masses.

Clockwork/linear dilaton: structure and phenomenology

The linear dilaton geometry in five dimensions, rediscovered recently in the continuum limit of the clockwork model, may offer a solution to the hierarchy problem which is qualitatively different from other extra-dimensional scenarios and leads to distinctive signatures at the LHC. We discuss the structure of the theory, in particular aspects of naturalness and UV completion, and then explore its phenomenology, suggesting novel strategies for experimental searches. In particular, we propose to analyze the diphoton and dilepton invariant mass spectra in Fourier space in order to identify an approximately periodic structure of resonant peaks. Among other signals, we highlight displaced decays from resonantly-produced long-lived states and high-multiplicity final states from cascade decays of excited gravitons.

Holography Beyond AdS

We continue our study of string theory in a background that interpolates between AdS3 in the infrared and a linear dilaton spacetime R1,1×Rϕ in the UV. This background corresponds via holography to a CFT2 deformed by a certain irrelevant operator of dimension (2,2). We show that for two point functions of local operators in the infrared CFT, conformal perturbation theory in this irrelevant operator has a finite radius of convergence in momentum space, and one can use it to flow up the renormalization group. The spectral density develops an imaginary part above a certain critical value of the spectral parameter; this appears to be related to the non-locality of the theory. In position space, conformal perturbation theory has a vanishing radius of convergence; the leading non-perturbative effect is an imaginary part of the two point function.

Motion and collision of particles in a rotating linear dilaton black hole

We study the motion of particles in the background of a four-dimensional linear dilaton black hole. We solve analytically the equations of motion of the test particles and we describe their motion. We show that the dilaton black hole acts as a particle accelerator by analyzing the energy in the center of mass (CM) frame of two colliding particles in the vicinity of its horizon. In particular we find that there is a critical value of the angular momentum, which depends on the string coupling, and a particle with this critical angular momentum can reach the inner horizon with an arbitrarily high CM energy. This is known as the Ba\~nados, Silk and West (BSW) process. We also show that the motion and collisions of particles have a similar behavior to the three-dimensional BTZ black hole. In fact, the photons can plunge into the horizon or escape to infinity, and they can not be deflected, while for massive particles there are no confined orbits of first kind, like planetary or circular orbits.

Exploring extra dimensions through inflationary tensor modes

Predictions of inflationary schemes can be influenced by the presence of extra dimensions. This could be of particular relevance for the spectrum of gravitational waves in models where the extra dimensions provide a brane-world solution to the hierarchy problem. Apart from models of large as well as exponentially warped extra dimensions, we analyze the size of tensor modes in the Linear Dilaton scheme recently revived in the discussion of the “clockwork mechanism”. The results are model dependent, significantly enhanced tensor modes on one side and a suppression on the other. In some cases we are led to a scheme of “remote inflation”, where the expansion is driven by energies at a hidden brane. In all cases where tensor modes are enhanced, the requirement of perturbativity of gravity leads to a stringent upper limit on the allowed Hubble rate during inflation.

Minkowski Solutions of IIB Supergravity

AbstractWe classify Minkowski4 solutions of IIB supergravity with an symmetry geometrically realized by an S2‐foliation in the remaining six dimensions. For the various cases of the classification, we reduce the supersymmetric system of equations to PDEs. These cases often accommodate systems of intersecting branes and half‐maximally supersymmetric AdS5, 6, 7 solutions when they exist. As an example, we analyze the AdS6 case in more detail, reducing the supersymmetry equations to a single cylindrical Laplace equation. We also recover an already known linear dilaton background dual to the (1, 1) Little String Theory (LST) living on NS5‐branes, and we find a new Minkowski5 linear dilaton solution from brane intersections. Finally, we also discuss some simple Minkowski4 solutions based on compact conformal Calabi‐Yau manifolds.

Matrix quantum mechanics on [formula omitted

We study Matrix Quantum Mechanics on the Euclidean time orbifold S1/Z2. Upon Wick rotation to Lorentzian time and taking the double-scaling limit this theory provides a toy model for a big-bang/big crunch universe in two dimensional non-critical string theory where the orbifold fixed points become cosmological singularities. We derive the MQM partition function both in the canonical and grand canonical ensemble in two different formulations and demonstrate agreement between them. We pinpoint the contribution of twisted states in both of these formulations either in terms of bi-local operators acting at the end-points of time or branch-cuts on the complex plane. We calculate, in the matrix model, the contribution of the twisted states to the torus level partition function explicitly and show that it precisely matches the world-sheet result, providing a non-trivial test of the proposed duality. Finally we discuss some interesting features of the partition function and the possibility of realising it as a τ-function of an integrable hierarchy.

The effective supergravity of little string theory

In this work we present the minimal supersymmetric extension of the five-dimensional dilaton-gravity theory that captures the main properties of the holographic dual of little string theory. It is described by a particular gauging of mathcal {N}=2 supergravity coupled with one vector multiplet associated with the string dilaton, along the U(1) subgroup of SU(2) R-symmetry. The linear dilaton in the fifth coordinate solution of the equations of motion (with flat string frame metric) breaks half of the supersymmetries to mathcal {N}=1 in four dimensions. Interest in the linear dilaton model has lately been revived in the context of the clockwork mechanism, which has recently been proposed as a new source of exponential scale separation in field theory.

Toverline{T} -deformations, AdS/CFT and correlation functions

A solvable irrelevant deformation of AdS3/CFT2 correspondence leading to a theory with Hagedorn spectrum at high energy has been recently proposed. It consists of a single trace deformation of the boundary theory, which is inspired by the recent work on solvable Toverline{T} deformations of two-dimensional CFTs. Thought of as a worldsheet σ-model, the interpretation of the deformed theory from the bulk viewpoint is that of string theory on a background that interpolates between AdS3 in the IR and a linear dilaton vacuum of little string theory in the UV. The insertion of the operator that realizes the deformation in the correlation functions produces a logarithmic divergence, leading to the renormalization of the primary operators, which thus acquire an anomalous dimension. We compute this anomalous dimension explicitly, and this provides us with a direct way of determining the spectrum of the theory. We discuss this and other features of the correlation functions in presence of the deformation.

Gauged U(1) clockwork theory

We consider the gauged U(1) clockwork theory with a product of multiple gauge groups and discuss the continuum limit of the theory to a massless gauged U(1) with linear dilaton background in five dimensions. The localization of the lightest state of gauge fields on a site in the theory space naturally leads to exponentially small effective couplings of external matter fields localized away from the site. We discuss the implications of our general discussion with some examples, such as mediators of dark matter interactions, flavor-changing B-meson decays as well as D-term SUSY breaking.

Clockwork Goldstone bosons

The clockwork mechanism has recently been proposed as a natural way to generate hierarchies among parameters in quantum field theories. The mechanism is characterized by a very specific pattern of spontaneous and explicit symmetry breaking, and the presence of new light states referred to as `gears'. In this paper we begin by investigating the self-interactions of these gears in a scalar clockwork model and find a parity-like selection rule at all orders in the fields. We then proceed to investigate how the clockwork mechanism can be realized in 5D linear dilaton models from the spontaneous symmetry breaking of a complex bulk scalar field. We also discuss how the clockwork mechanism is manifest in the scalar components of 5D gauge theories in the linear dilaton model, and build their 4D deconstructed analogue. Finally we discuss attempts at building both 4D and 5D realizations of a non-abelian scalar clockwork mechanism, where in the latter we consider scenarios in which the Goldstone bosons arise from 5D scalar and 5D gauge fields.

Trisecting non-Lagrangian theories

We propose a way to define and compute invariants of general smooth 4-manifolds based on topological twists of non-Lagrangian 4d mathcal{N}=2kern0.5em mathrm{and}kern0.5em mathcal{N}=3 theories in which the problem is reduced to a fairly standard computation in topological A-model, albeit with rather unusual targets, such as compact and non-compact Gepner models, asymmetric orbifolds, mathcal{N}=left(2,2right) linear dilaton theories, “self-mirror” geometries, varieties with complex multiplication, etc.

Menagerie of AdS2 boundary conditions

We consider different sets of AdS2 boundary conditions for the Jackiw-Teitelboim model in the linear dilaton sector where the dilaton is allowed to fluctuate to leading order at the boundary of the Poincaré disk. The most general set of boundary conditions is easily motivated in the gauge theoretic formulation as a Poisson sigma model and has an mathfrak{s}mathfrak{l}(2) current algebra as asymptotic symmetries. Consistency of the variational principle requires a novel boundary counterterm in the holographically renormalized action, namely a kinetic term for the dilaton. The on-shell action can be naturally reformulated as a Schwarzian boundary action. While there can be at most three canonical boundary charges on an equal-time slice, we consider all Fourier modes of these charges with respect to the Euclidean boundary time and study their associated algebras. Besides the (centerless) mathfrak{s}mathfrak{l}(2) current algebra we find for stricter boundary conditions a Virasoro algebra, a warped conformal algebra and a mathfrak{u}(1) current algebra. In each of these cases we get one half of a corresponding symmetry algebra in three-dimensional Einstein gravity with negative cosmological constant and analogous boundary conditions. However, on-shell some of these algebras reduce to finite-dimensional ones, reminiscent of the on-shell breaking of conformal invariance in SYK. We conclude with a discussion of thermodynamical aspects, in particular the entropy and some Cardyology.

Varying dilaton as a tracer of classical string interactions

We analyze tree-level string amplitudes in a linear dilaton background, motivated by its use as a gauge-invariant tracer of string interactions in scattering experiments and its genericity among simple perturbative string theory limits. A simple case is given by a lightlike dependence for the dilaton. The zero mode of the embedding coordinate in the direction of dilaton variation requires special care. Employing Gaussian wave packets and a well-defined modification of the dilaton profile far from the dominant interaction region, we obtain finite results which explicitly reproduce the interaction timescales expected from joining and splitting interactions involving oscillating strings in simple string scattering processes. There is an interesting interplay between the effects of the linear dilaton and the $i\epsilon$ prescription. In more general circumstances this provides a method for tracing the degree of non-locality in string interactions, and it gives a basis for further studies of perturbative supercritical string theory at higher loop order.

Long-range nonlocality in six-point string scattering: Simulation of black hole infallers

We set up a tree-level six point scattering process in which two strings are separated longitudinally such that they could only interact directly via a non-local spreading effect such as that predicted by light cone gauge calculations and the Gross-Mende saddle point. One string, the `detector', is produced at a finite time with energy $E$ by an auxiliary $2\to 2$ sub-process, with kinematics such that it has sufficient resolution to detect the longitudinal spreading of an additional incoming string, the `source'. We test this hypothesis in a gauge-invariant S-matrix calculation convolved with an appropriate wavepacket peaked at a separation $X$ between the central trajectories of the source and produced detector. The amplitude exhibits support for scattering at the predicted longitudinal separation $X\sim\alpha' E$, in sharp contrast to the analogous quantum field theory amplitude (whose support manifestly traces out a tail of the position-space wavefunction). The effect arises in a regime in which the string amplitude is not obtained as a convergent sum of such QFT amplitudes, and has larger amplitude than similar QFT models (with the same auxiliary four point amplitude). In a linear dilaton background, the amplitude depends on the string coupling as expected if the scattering is not simply occuring on the wavepacket tail in string theory. This manifests the scale of longitudinal spreading in a gauge-invariant S-matrix amplitude, in a calculable process with significant amplitude. It simulates a key feature of the dynamics of time-translated horizon infallers.

From 6D superconformal field theories to dynamic gauged linear sigma models

Compactifications of 6D superconformal field theories (SCFTs) on four-manifolds generate a large class of novel 2d quantum field theories. We consider in detail the case of the rank one simple non-Higgsable cluster 6D SCFTs. On the tensor branch of these theories, the gauge group is simple and there are no matter fields. For compactifications on suitably chosen Kahler surfaces, we present evidence that this provides a method to realize 2d SCFTs with N = (0,2) supersymmetry. In particular, we find that reduction on the tensor branch of the 6D SCFT yields a description of the same 2d fixed point that is described in the UV by a gauged linear sigma model (GLSM) in which the parameters are promoted to dynamical fields, that is, a "dynamic GLSM" (DGLSM). Consistency of the model requires the DGLSM to be coupled to additional non-Lagrangian sectors obtained from reduction of the anti-chiral two-form of the 6D theory. These extra sectors include both chiral and anti-chiral currents, as well as spacetime filling non-critical strings of the 6D theory. For each candidate 2d SCFT, we also extract the left- and right-moving central charges in terms of data of the 6D SCFT and the compactification manifold.

Mathrm{T}overline{mathrm{T}} and LST

It was recently shown that the theory obtained by deforming a general two dimensional conformal theory by the irrelevant operator Toverline{T} is solvable. In the context of holography, a large class of such theories can be obtained by studying string theory on AdS3. We show that a certain single trace Toverline{T} deformation of the boundary CFT2 gives rise in the bulk to string theory in a background that interpolates between AdS3 in the IR and a linear dilaton spacetime in the UV, i.e. to a two dimensional vacuum of Little String Theory. This construction provides holographic duals for a large class of vacua of string theory in asymptotically linear dilaton spacetimes, and sheds light on the UV behavior of Toverline{T} deformed CFT2. It may provide a step towards holography in flat spacetime.

Viscosity for anisotropic Reissner-Nordström black branes

We investigate the behavior of shear viscosity in the presence of small anisotropy and a finite chemical potential. First, we construct an anisotropic Reissner Nordstr\"om black brane in five dimensions in a simple Einstein-Maxwell theory with a small linear dilaton. This solution is characterized by three mass scales: anisotropy $\ensuremath{\rho}$, temperature $T$, and chemical potential $\ensuremath{\mu}$. We find this solution up to second order in the dilaton anisotropy parameter $\ensuremath{\rho}$. This black brane solution corresponds to an anisotropic phase where the anisotropy is small compared to the temperature and chemical potential. We find that in this anisotropic phase, some components of the anisotropic shear viscosity tensor, which are spin one with respect to the residual symmetry after breaking rotational invariance, violates the KSS bound ($\frac{\ensuremath{\eta}}{s}\ensuremath{\ge}\frac{1}{4\ensuremath{\pi}}$) proposed by Kovtun, Son, and Starinets. We identify the regions of the parameter space where these violations are significant. We carry out a similar analysis in four dimensions and find a similar violation of the KSS bound for the spin one components to demonstrate the generality of the result. Our results are particularly relevant in the context of strongly coupled systems found in nature. We also provide an intuitive understanding of the results using dimensional reduction and a Boltzmann calculation in a weakly coupled version of a similar system. The Boltzmann analysis performed in a system of weakly interacting particles in a linear potential also shows that components of the viscosity tensor may be reduced. It is intriguing that the Boltzmann analysis also predicts the corrections to be negative and that too in a manner similar to the anisotropic strongly coupled theories with smooth gravity duals.