We present two-dimensional gauged Lifshitz scalar field theories by considering the duality relation between the source current and the Noether current. Requiring the duality partially, we obtain a gauged model which recovers the bosonized Schwinger model for the IR limit. For the exact duality, however, the source current is not conserved, which means that the resulting theory is anomalous, so that the number of degrees of freedom is increased. The second model is consistently formulated by adding the Wess-Zumino type action to maintain the gauge invariance.
We study the gauged Landau-Lifshitz model in which a suitably chosen triplet of background scalar fields is included. It is shown that the model admits solitonic configurations.
We fermionize the two-dimensional free Lifshitz scalar field in order to identify what the gauge covariant couplings are, and then they are bosonized back to get the gauged Lifshitz scalar field theories. We show that they give the same physical modes with those of the corresponding Lorentz invariant gauged scalar theories, although the dispersion relations are different.
We present a gauged Lifshitz Lagrangian including second and forth order spatial derivatives of the scalar field and a Chern-Simons term, and study non-trivial solutions of the classical equations of motion. While the coefficient beta of the forth order term should be positive in order to guarantee positivity of the energy, the coefficient alpha of the quadratic one need not be. We investigate the parameter domains finding significant differences in the field behaviors. Apart from the usual vortex field behavior of the ordinary relativistic Chern-Simons-Higgs model, we find in certain paramete…
We discuss two classes of non-supersymmetric interpolating solutions in N=2, D=4 gauged supergravity, that flow from either a z=2 Lifshitz geometry or a conformal AdS background to the near-horizon geometry of a Nernst brane. We obtain these solutions by constructing a z=2 supersymmetric Lifshitz solution in the STU model from a first-order rewriting of the action, then lifting it up to a five-dimensional background and subsequently modifying this five-dimensional solution by a two-parameter family of deformations. Under reduction, these give four-dimensional non-supersymmetric Nernst brane so…
We consider the subset of gauged maximal supergravities that consists of the SO(n+1) gauge fields A^{ij} and the scalar deformation T^{ij} of the S^n in the spherical reduction of M-theory or type IIB. We focus on the Abelian Cartan subgroup and the diagonal entries of T^{ij}. The resulting theories can be viewed as the STU models with additional hyperscalars. We find that the theories with only one or two such vectors can be generalized naturally to arbitrary dimensions. The same is true for the D=4 or 5 Einstein-Maxwell theory with such a hyperscalar. The gauge fields become massive, determi…
We find infinite families of supersymmetric solutions of four dimensional, N=2 gauged supergravity with Lifshitz, Schrodinger and also AdS symmetries. We focus on the canonical example of a single hypermultiplet and a single vector multiplet and find that the spectrum of solutions depends crucially on whether the gaugings are electric or magnetic but to a far milder extent on the strength of the gaugings. For purely electric or purely magnetic gaugings we generically find Lifshitz solutions, while for a mixed gauging we find Schrodinger and AdS solutions. For some of the gaugings the theory ha…
We construct gravity solutions describing renormalization group flows relating relativistic and non-relativistic conformal theories. We work both in a simple phenomenological theory with a massive vector field, and in an N=4, d=6 gauged supergravity theory, which can be consistently embedded in string theory. These flows offer some further insight into holography for Lifshitz geometries: in particular, they enable us to give a description of the field theory dual to the Lifshitz solutions in the latter theory. We also note that some of the AdS and Lifshitz solutions in the N=4, d=6 gauged supe…
Magnetic BPS string solutions preserving quarter of supersymmetry are obtained for all abelian gauged d=5 N=2 supergravity theories coupled to vector supermultiplets. Due to a ``generalised Dirac quantization'' condition satisfied by the minimized magnetic central charge, the string metric takes a universal form for all five dimensional gauged theories.
We consider two different versions of gauged WZW theories with the exceptional groups and gauged with any of theirs null subgroups. By constructing suitable automorphism, we establish the equivalence of these two theories. On the other hand our automorphism, relates the two dual irreducible Riemannian globally symmetric spaces with different characters based on the corresponding exceptional Lie groups.
In this paper, we will incorporation the generalized uncertainty principle into field theories with Lifshitz scaling. We will first construct both bososnic and fermionic theories with Lifshitz scaling based on generalized uncertainty principle. After that we will incorporate the generalized uncertainty principle into an non-abelian gauge theory with Lifshitz scaling. We will observe that even though the action for this theory is non-local, it is invariant under local gauge transformations. We will also perform the stochastic quantization of this Lifshitz fermionic theory based generalized unce…
We construct fermionic Lagrangians with anisotropic scaling z=2, the natural counterpart of the usual z=2 Lifshitz field theories for scalar fields. We analyze the issue of chiral symmetry, construct the Noether axial currents and discuss the chiral anomaly giving explicit results for two-dimensional case. We also exploit the connection between detailed balance and the dynamics of Lifshitz theories to find different z=2 fermionic Lagrangians and construct their supersymmetric extensions.
We calculate the one-loop effective potential for Horava-Lifshitz-like QED with an arbitrary critical exponent within different approaches and discuss its gauge dependence.
Lagrangian gauge theories with a z=2 Lifshitz scaling provide a family of interacting, asymptotically free five-dimensional field theories. We examine some of their quantum properties, extending previous results to include matter. We present no-go theorems that, in the absence of constraints, such theories cannot admit a spinorial supersymmetry or a boost symmetry. However, we argue that there exist renormalization group flows whose fixed points can admit supersymmetry and boosts, i.e. super-Schrodinger symmetry. We also present examples of Lifshitz gauge theories with a scalar supersymmetry.
In this note we discuss the classification of duality orbits of N = 8 gauged supergravity models. Using tensor classifiers, we show that there is a one-parameter family of inequivalent SO(8) gauged supergravity theories. We briefly discuss the couplings of such models and show that, although the maximally symmetric vacuum has the same quadratic spectrum, the supersymmetry transformations, the couplings and the scalar potential are parameter dependent. We also comment on the possible M-theory uplift and on the meaning of the parameter for the dual gauge theories.
We calculate the one-loop effective potential for Horava-Lifshitz-like QED and Yukawa-like theory for arbitrary values of the critical exponent and the space-time dimension.
We study possibilities of string theory embeddings of the gravity duals for non-relativistic Lifshitz-like theories with anisotropic scale invariance. We search classical solutions in type IIA and eleven-dimensional supergravities which are expected to be dual to (2+1)-dimensional Lifshitz-like theories. Under reasonable ansaetze, we prove that such gravity duals in the supergravities are not possible. We also discuss a possible physical reason behind this.
We calculate the one-loop effective potential at finite temperature for the Horava-Lifshitz-like QED and Yukawa-like theories for arbitrary values of the critical exponent and the space-time dimension. Additional remarks on the zero temperature situation are also presented.
A new method of gauging of WZNW models is presented, leading to a class of exact string solutions with a target space metric of Minkowskian signature. The corresponding models may be interpreted as $σ$-model analogues of the Toda field theories.
Canonical quantisation of the free-field zero modes q, p on a half-line p>0 provides for WZNW coset theories self-adjoint vertex operatorson account of hidden symmetries generated by an S-matrix.
In this paper three dimensional higher spin theories in the Chern-Simons formulation with gauge algebra $sl(N,R)$ are investigated which have Lifshitz symmetry with scaling exponent $z$. We show that an explicit map exists for all $z$ and $N$ relating the Lifshitz Chern-Simons theory to the $(n,m)$ element of the KdV hierarchy. Furthermore we show that the map and hence the conserved charges are independent of $z$. We derive these result from the Drinfeld-Sokolov formalism of integrable systems.
We readdress the question of whether any universal upper bound exists on the square mass m^2 of the lightest scalar around a supersymmetry breaking vacuum in generic N=2 gauged supergravity theories for a given gravitino mass m_3/2 and cosmological constant V. We review the known bounds which apply to theories with restricted matter content from a new perspective. We then extend these results to theories with both hyper and vector multiplets and a gauging involving only one generator, for which we show that such a bound exists for both V>0 and V<0. We finally argue that there is no bound for t…
The 2+1 dimensional quantum Lifshitz model can be generalised to a class of higher dimensional free field theories that exhibit Lifshitz scaling. When the dynamical critical exponent equals the number of spatial dimensions, equal time correlation functions of scaling operators in the generalised quantum Lifshitz model are given by a d-dimensional higher-derivative conformal field theory. Autocorrelation functions in the generalised quantum Lifshitz model in any number of dimensions can on the other hand be expressed in terms of autocorrelation functions of a two-dimensional conformal field the…
In this work, we develop a normal product algorithm suitable to the study of anisotropic field theories in flat space, apply it to construct the symmetries generators and describe how their possible anomalies may be found. In particular, we discuss the dilatation anomaly in a scalar model with critical exponent z=2 in six spatial dimensions.
Within the superfield approach, we formulate two different extensions of the Wess-Zumino model and super-QED with Horava-Lifshitz-like additive terms, discuss their quantum properties and calculate lower contributions to the effective action. In the case of the gauge theory, the one-loop effective potential turns out to be gauge independent.
We study the canonical energy-momentum tensor of the spherically symmetric $U(1)$ gauged Q-ball configurations in the two-component Fridberg-Lee-Sirlin-Maxwell model, and in the one-component scalar model with a sixtic potential. We evaluate the distributions of the corresponding shear forces and pressure and study the stability criteria for these solutions. It is shown that the electrostatic repulsion may destabilize the $U(1)$ gauged Q-balls. However, in the limiting case of the Fridberg-Lee-Sirlin-Maxwell model with a long ranged real scalar component, the gauged Q-balls always remain stabl…
In this paper, we analyse the stability of extremal black brane horizons with homogeneous symmetry in the spatial directions in five dimensional gauged supergravity, under the fluctuations of the scalar fields about their attractor values. We examine the scalar fluctuation equations at the linearised level and demand that the fluctuations vanish as one approaches the horizon. Imposing certain restrictions on the Killing vectors used for gauging we find that the necessary conditions for stability are satisfied only by a subclass of the Bianchi metrics whose symmetry group factorises into a two …
We propose candidate gravity duals for a class of non-Abelian z=2 Lifshitz Chern-Simons (LCS) gauge theories studied by Mulligan, Kachru and Nayak. These are nonrelativistic gauge theories in 2+1 dimensions in which parity and time-reversal symmetries are explicitly broken by the presence of a Chern-Simons term. We show that these field theories can be realized as deformations of DLCQ N=4 super Yang-Mills theory. Using the holographic dictionary, we identify the bulk fields that are dual to these deformations. The geometries describing the groundstates of the non-Abelian LCS gauge theories rea…
We construct supergravity solutions dual to twisted field theories that are the worldvolume theories of D4-branes wrapped on 2, 3-cycles, and NS-fivebranes on 3-cycles. We first obtain the solutions for the Romans' six-dimensional gauged supergravity theories and then up-lift them to ten dimensions. In particular, we find solutions for field configurations with either non-Abelian fields or B-fields being excited. One of these solutions, in the massless case, is up-lifted to the massless type IIA string theory. This is the first example of such a kind. The cases studied provide new examples of …
Recently, we have studied the general Virasoro construction at one loop in the background of the general non-linear sigma model. Here, we find the action formulation of these new conformal field theories when the background sigma model is itself conformal. In this case, the new conformal field theories are described by a large class of new spin-two gauged sigma models. As examples of the new actions, we discuss the spin-two gauged WZW actions, which describe the conformal field theories of the generic affine-Virasoro construction, and the spin-two gauged g/h coset constructions. We are able to…
We study holographically Lifshitz-scaling theories with broken symmetries. In order to do this, we set up a bulk action with a complex scalar and a massless vector on a background which consists in a Lifshitz metric and a massive vector. We first study separately the complex scalar and the massless vector, finding a similar pattern in the two-point functions that we can compute analytically. By coupling the probe complex scalar to the background massive vector we can construct probe actions that are more general than the usual Klein--Gordon action. Some of these actions have Galilean boost sym…
We study Einstein-Maxwell-dilaton theories with a cosmological constant and U(1)^N gauge symmetry, considering metrics asymptotically approaching the Lifshiftz metric. We study the dependence of the phase diagram on the value of the dynamical exponent. Along the way, we apply holographic renormalization and propose a counterterm valid for arbitrary dimension and dynamical exponent in our setup.
The Wess-Zumino-Witten (WZW) theory has a global symmetry denoted by $G_L\otimes G_R$. In the standard gauged WZW theory, vector gauge fields (\ie\ with vector gauge couplings) are in the adjoint representation of the subgroup $H \subset G$. In this paper, we show that, in the conformal limit in two dimensions, there is a gauged WZW theory where the gauge fields are chiral and belong to the subgroups $H_L$ and $H_R$ where $H_L$ and $H_R$ can be different groups. In the special case where $H_L=H_R$, the theory is equivalent to vector gauged WZW theory. For general groups $H_L$ and $H_R$, an exa…
In this article we review recent progress on the holographic modelling of field theories with Lifshitz symmetry. We focus in particular on the holographic dictionary for Lifshitz backgrounds - the relationship between bulk fields and boundary operators, operator correlation functions and underlying geometrical structure. The holographic dictionary is essential in identifying the universality class of strongly coupled Lifshitz theories described by gravitational models.
In this work, we propose three different modified relativistic particles. In the first case, we propose a particle with metrics depending on the momenta and we show that the quantum version of these systems includes different field theories, as Lifshitz field theories. As a second case we propose a particle that implies a modified symplectic structure and we show that the quantum version of this system gives different noncommutative space-times, for example the Snyder space-time. In the third case, we combine both structures before mentioned, namely noncommutative space-times and momentum depe…
In this paper, we analyze the fermionic Casimir effects associated with a massless quantum field in the context of Lorentz symmetry violation approach based on Horava-Lifshitz methodology. In order to obtain these observables, we impose the standard MIT bag boundary condition on the fields on two large and parallel plates. Our main objectives are to investigate how the Casimir energy and pressure depend on the parameter associated with the breaking of Lorentz symmetry.
BPS instantons are discussed in Lifshitz-type anisotropic field theories. We consider generalizations of the sigma model/Yang-Mills instantons in renormalizable higher dimensional models with the classical Lifshitz scaling invariance. In each model, BPS instanton equation takes the form of the gradient flow equations for "the superpotential" defining "the detailed balance condition". The anisotropic Weyl rescaling and the coset space dimensional reduction are used to map rotationally symmetric instantons to vortices in two-dimensional anisotropic systems on the hyperbolic plane. As examples, w…
We consider the one-loop effective potential at zero and finite temperature in field theories with anisotropic space-time scaling, with critical exponent $z=2$, including both scalar and gauge fields. Depending on the relative strength of the coupling constants for the gauge and scalar interactions, we find that there is a symmetry breaking term induced at one-loop at zero temperature and we find symmetry restoration through a first-order phase transition at high temperature.
We discuss the ultraviolet sector of 3+1 dimensional Lifshitz-type anisotropic higher derivative scalar, fermion and gauge field theories, with anisotropy exponent z=3 and with explicit breaking of Lorentz symmetry. By discarding from the action all momentum dependent vertex operators, which is essential to avoid phenomenologically unacceptable deformations of the light cone, we find that renormalizable scalar self-interaction and Yukawa-like couplings are, in general, asymptotically free. However, the requirement of cancelling momentum dependent vertex operators is incompatible with gauge sym…
This paper is devoted to the construction of new type of f(R) theories of gravity that are based on the principle of detailed balance. We discuss two versions of these theories with and without the projectability condition.
We consider three-dimensional maximally superconformal Bagger-Lambert-Gustavsson (BLG) theory and its topologically gauged version (constructed recently in arXiv:0809.4478 [hep-th]) in the light-cone gauge. After eliminating the entire Chern-Simons gauge field, the ungauged BLG theory looks more conventional and, apart from the order of the interaction terms, resembles N=4 super-Yang-Mills theory in four dimensions. The light-cone superspace version of the BLG theory is given to quadratic and quartic order and some problems with constructing the sixth order interaction terms are discussed. In …
This note is devoted to the study of Hamiltonian formalism of modified F(R) Horava-Lifshitz theories of gravity that were proposed recently in arXiv:1001.4102[hep-th]. We also study Hamiltonian formulation of the healthy extended Horava-Lifshitz gravities and show that these theories have many unusual and interesting properties.
A class of conformally flat and asymptotically anti-de Sitter geometries involving profiles of scalar fields is studied from the point of view of gauged supergravity. The scalars involved in the solutions parameterise the SL(N,R)/SO(N) submanifold of the full scalar coset of the gauged supergravity, and are described by a symmetric potential with a universal form. These geometries descend via consistent truncation from distributions of D3-branes, M2-branes, or M5-branes in ten or eleven dimensions. We exhibit analogous solutions asymptotic to AdS_6 which descend from the D4-D8-brane system. We…
The low-energy effective theories describing string compactifications in the presence of fluxes are so-called gauged supergravities: deformations of the standard abelian supergravity theories. The deformation parameters can be identified with the various possible (geometric and non-geometric) flux components. In these lecture notes we review the construction of gauged supergravities in a manifestly duality covariant way and illustrate the construction in several examples.
We study $SU(2)$ gauge theories coupled to $(A_1,D_N)$ theories with or without a fundamental hypermultiplet. For even $N$, a formula for the contribution of $(A_1,D_N)$ to the Nekrasov partition function was recently obtained by us with Y.~Sugawara and T.~Uetoko. In this paper, we generalize it to the case of odd $N$ in the classical limit, under the condition that the relevant couplings and vacuum expectation values of Coulomb branch operators of $(A_1,D_N)$ are all turned off. We apply our formula to the $(A_2,A_5)$ theory to find that its prepotential is related to that of the $SU(2)$ gaug…
Nonlinear sigma models arise in supergravity theories with or without matter couplings in various dimensions and they are important in understanding the duality symmetries of M-theory. With this motivation in mind, we review the salient features of gauged and ungauged nonlinear sigma models with or without Wess-Zumino terms for general target spaces in a minimal as well as lifted formulation. Relevant to the question of finding interesting vacua of gauged supergravity theories is the highly constrained potential which arises naturally in these theories. Motivated by this fact, we derive a gene…
Via the AdS/CFT correspondence, ground states of field theories at finite charge density are mapped to extremal black brane solutions. Studies of simple gravity + matter systems in this context have uncovered wide new classes of extremal geometries. The Lifshitz metrics characterising field theories with non-trivial dynamical critical exponent $z \neq 1$ emerge as one common endpoint in doped holographic toy models. However, the Lifshitz horizon exhibits mildly singular behaviour - while curvature invariants are finite, there are diverging tidal forces. Here we show that in some of the simples…
We show that one can construct D-branes in parafermionic and WZW theories (and their orbifolds) which have very natural geometrical interpretations, and yet are not automatically included in the standard Cardy construction of D-branes in rational conformal field theory. The relation between these theories and their T-dual description leads to an analogy between these D-branes and the familiar A-branes and B-branes of N=2 theories.
In this note, we discuss the renormalizability of Horava-Lifshitz-type gravity theories. Using the fact that Horava-Lifshitz gravity is very closely related to the stochastic quantization of topologically massive gravity, we show that the renormalizability of HL gravity only depends on the renormalizability of topologically massive gravity. This is a consequence of the BRST and time-reversal symmetries pertinent to theories satisfying the detailed balance condition.
We study the SO(4)-symmetric solution of the five-dimensional SU(2) x U(1) gauged N=4 supergravity theory obtained in [hep-th/0101202]. This solution contains purely magnetic non-Abelian and electric Abelian fields. It can be interpreted as a reduction of seven-dimensional gauged supergravity on a torus, which comes from type IIB supergravity on S^3. We also show how to obtain that solution from six-dimensional Romans' theory on a circle. We then up-lift the solution to massless type IIA supergravity. The dual gauge field theory is twisted and is defined on the worldvolume of a NS-fivebrane wr…
By coupling {\cal N}=8 superconformal matter to {\cal N}=8 superconformal Chern-Simons gravity in three dimensions we obtain theories with novel terms in the scalar potential leading to AdS_3 solutions and superconformal symmetry breaking. If we start from the theory derived by Bagger, Lambert and Gustavsson, our coupled theory either inherits the SO(4) gauge group or reduces it to SO(3). If the construction is instead based on a free matter theory we find that the gravitational topological gauging also requires the introduction of a Chern-Simons gauge sector resulting in a consistent theory f…
We continue our study of the Lorentz breaking string theories. These theories are defined as string theory with modified Hamiltonian constraint which breaks the Lorentz symmetry of target space-time. We analyze properties of this theory in the target space-time that possesses isometry along one direction. We also derive the T-duality rules for Lorentz breaking string theories and show that they are the same as that of Buscher's T-duality for the relativistic strings.
In this work we extend the results of previous derivations of Seiberg-like dualities (level-rank duality) between gauged Wess-Zumino-Witten theories. The arguments in use to identify a potential dual for the supersymmetric WZW theory based on the coset $\frac{U(N+M)_k}{U(N)_k}$ can be extended to be applied to a wider variety of gauge groups, notably $\frac{USp(2N+2M)_{2k}}{USp(2N)_{2k}}$ and $\frac{SO(2N+2M)_{2k}}{SO(2N)_{2k}}$, which will be dealt with briefly. Most interestingly, non-supersymmetric versions of the latter theories can also be shown to have duals in a similar fashion. These r…
We formulate all the five dimensional gauged maximal supergravity theories as non-linear realisations of the semi-direct product of E_{11} and a set of generators which transform according to the first fundamental representation l of E_{11}. The latter introduces a generalised space-time which plays a crucial role for these theories. We derive the E_{11} and l transformations of all the form fields and their dynamics. We also formulate the five dimensional gauged supergravity theories using the closure of the supersymmetry algebra. We show that this closes on the bosonic field content predicte…
In this thesis we study maximally supersymmetric solutions of gauged supergravity theories, with special focus on anti-de Sitter solutions. The latter are relevant in the context of the AdS/CFT correspondence. In the first part we classify all maximally supersymmetric solutions of all gauged or deformed supergravity theories in $D \geq 3$ space-time dimensions. In the second part we exclusively study maximally supersymmetric AdS$_D$ solutions of gauged supergravities in dimensions $D \geq 4$. We discuss the structure of the allowed gauge groups as well as possible supersymmetry preserving defo…
Generalised Scherk-Schwarz reductions in which compactification on a circle is accompanied by a twist with an element of a global symmetry G typically lead to gauged supergravities and are classified by the monodromy matrices, up to conjugation by the global symmetry. For compactifications of IIB supergravity on a circle, G=SL(2,R) and there are three distinct gauged supergravities that result, corresponding to monodromies in the three conjugacy classes of SL(2,R). There is one gauging of the compact SO(2) subgroup of the SL(2,R) and two distinct gaugings of non-compact SO(1,1) subgroups, embe…
We study gauged linear sigma models for noncompact Calabi-Yau manifolds described as a line bundle on a hypersurface in a projective space. This gauge theory has a unique phase if the Fayet-Iliopoulos parameter is positive, while there exist two distinct phases if the parameter is negative. We find four massless effective theories in the infrared limit, which are related to each other under the Calabi-Yau/Landau-Ginzburg correspondence and the topology change. In the T-dual theory, on the other hand, we obtain two types of exact massless effective theories: One is the sigma model on a newly ob…
Bosonic quantum field theories with holomorphic action functionals are realized by two types of constructions involving supersymmetric quantum field theories, compactified on an interval in one type and compactified on a disk and deformed in the other. We establish the equivalence between the two types of constructions by reducing the disk to the interval and the interval to a point. As examples, we discuss constructions of zero-dimensional gauged sigma model, gauged quantum mechanics, gauged symplectic bosons in two dimensions, and Chern-Simons theory and its higher-dimensional variants.
We obtain relaxation times for field theories with Lifshitz scaling and with holographic duals Einstein-Maxwell-Dilaton gravity theories. This is done by computing quasinormal modes of a bulk scalar field in the presence of Lifshitz black branes. We determine the relation between relaxation time and dynamical exponent z, for various values of boundary dimension d and operator scaling dimension. It is found that for d>z+1, at zero momenta, the modes are non-overdamped, whereas for d<=z+1 the system is always overdamped. For d=z+1 and zero momenta, we present analytical results.
We consider Hanany-Witten setups of 3- and 5-branes in type IIB string theory that realize N=(1,0),(2,0) and (1,1) gauged WZW models in 1+1 dimensions. The gauged WZW models arise as theories residing on the boundary of D3 branes ending on D5 branes. From the point of view of low energy dynamics the D5 branes play the role of half-BPS co-dimension-1 defects (domain walls) in 3d N=1 or N=2 Chern-Simons theories. Extending the analysis of previous works on the subject of boundary conditions in (supersymmetric) Chern-Simons theory, we discuss in detail the field theory construction of a large cla…
