T a Larsson
It is shown that the ternary Virasoro-Witt algebra of Curtright, Fairlie and Zachos can be constructed by applying the Nambu commutator to the vect(1) realization on scalar densities. This construction is generalized to vect(d), but the corresponding 3-algebra fails to close.
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We classify non-trivial (non-central) extensions of the group $Diff^+(S^1)$ of all diffeomorphisms of the circle preserving its orientation and of the Lie algebra $Vect (S^1)$ of vector fields on $S^1$, by the modules of tensor-densities on $S^1$. The result is: 4 non-trivial extensions of $Diff^+(S^1)$ and 7 non-trivial extensions of $Vect (S^1)$. Analogous results hold for the Virasoro group and the Virasoro algebra. We also classify central extensions of constructed Lie algebras. CPT-94/P.3024
A current of the deformed Virasoro algebra is identified with the Zamolodchikov-Faddeev operator for the basic scalar particle in the XYZ model.
We discuss the quantization of a scalar field in three-dimensional asymptotic de Sitter space. We obtain explicit expressions for the Noether currents generating the isometry group in terms of the modes of the scalar field and the Liouville gravitational field. We extend the SL(2,C) algebra of the Noether charges to a full Virasoro algebra by introducing non-local conserved charges. The Virasoro algebra has the expected central charge in the weak coupling limit (large central charge c=3l/2G, where l is the dS radius and G is Newton's constant). We derive the action of the Virasoro charges on s…
In this work we apply the lightcone bootstrap to a four-point function of scalars in two-dimensional conformal field theory. We include the entire Virasoro symmetry and consider non-rational theories with a gap in the spectrum from the vacuum and no conserved currents. For those theories, we compute the large dimension limit (h/c>>1) of the OPE spectral decomposition of the Virasoro vacuum. We then propose a kernel ansatz that generalizes the spectral decomposition beyond h/c>>1. Finally, we estimate the corrections to the OPE spectral densities from the inclusion of the lightest operator in t…
We derive new constraints on the spectrum of two-dimensional conformal field theories with central charge $c>1.$ Employing the pillow representation of the four point correlator of identical scalars with dimension $Δ_{\mathcal{O}}$ and positivity of the coefficients of its expansion in the elliptic nome we place central charge dependent bounds on the dimension of the first excited Virasoro primary the scalar couples to, in the form $Δ_1<f(c,Δ_{\mathcal{O}}).$ We give an analytic expression for $f(c,Δ_{\mathcal{O}})$ and write down transcendental equations that significantly improve the analyti…
Strominger has derived the Bekenstein-Hawking entropy of the BTZ black hole using asymptotic Virasoro algebra. We apply Strominger's method to a black hole solution found by Martinez and Zanelli (MZ). This is a solution of three-dimensional gravity with a conformal scalar field. The solution is not $AdS_3$, but it is asymptotically $AdS_3$; therefore, it has the asymptotic Virasoro algebra. We compute the central charge for the theory and compares Cardy's formula with the Bekenstein-Hawking entropy. It turns out that the functional form does agree, but the overall numerical coefficient does no…
A conformal field theory can be recovered, via the Kontsevich-Miwa transform, as a solution to the Virasoro constraints on the KP tau function. That theory, which we call KM CFT, consists of d \leq 1 matter plus a scalar and a dressing prescription: Δ= 0 for every primary field. By adding a spin-1 bc system the KM CFT provides a realization of the N=2 twisted topological algebra. The other twist of the corresponding untwisted N=2 superconformal theory is a DDK realization of the N=2 twisted topological algebra. Talk given by Beatriz Gato-Rivera at the "28th International Symposium on the Theor…
In this note we demonstrate that the algebra associated with coordinate transformations might contain the origins of a scalar field that can behave as an inflaton and/or a source for dark energy. We will call this particular scalar field the diffeomorphism scalar field. In one dimension, the algebra of coordinate transformations is the Virasoro algebra while the algebra of gauge transformations is the Kac-Moody algebra. An interesting representation of these algebras corresponds to certain field theories that have meaning in any dimension. In particular the so called Kac-Moody sector correspon…
By applying the stress-tensor-scalar operator product expansion (OPE) twice, we search for algebraic structures in $d=4$ conformal field theories (CFTs) with a pure Einstein gravity dual. We find that a rescaled mode operator defined by an integral of the stress tensor $T^{++}$ on a $d=2$ plane satisfies a Virasoro-like algebra when the dimension of the scalar is large. The structure is enhanced to include a Kac-Moody-type algebra if we incorporate the $T^{--}$ component. In our scheme, the central terms are finite. It remains challenging to directly compute the stress-tensor sector of $d=4$ s…
The cosmological field equations sourced by a self-interacting scalar field are dynamically equivalent to a closed system of equations obtained by applying the moment method to non-linear Schrödinger equations possessing an underlying non-relativistic conformal $SL(2,\mathbb{R})$ symmetry. We consider the one-dimensional, quintic Schrödinger equation relevant to strongly repulsive, dilute Bose gases. The action of the diffeomorphism group on the space of Schrödinger operators generates an harmonic trapping potential that can be identified with the kinetic energy of the cosmological scalar fiel…
Using the {\it off-shell} Noether current and potential we compute the entropy for the AdS black holes in new massive gravity. For the non-extremal BTZ black holes by implementing the so-called stretched horizon approach we reproduce the correct expression for the horizon entropy. For the extremal case, we adopt standard formalism in the AdS/CFT correspondence and reproduce the corresponding entropy by computing the central extension term on the asymptotic boundary of the near horizon geometry. We explicitly show the invariance of the angular momentum along the radial direction for extremal as…
Prior work using gauge/gravity duality has established the existence of a quantum critical point in the phase diagram of 3+1-dimensional gauge theories at finite charge density and background magnetic field. The critical theory, obtained by tuning the dimensionless charge density to magnetic field ratio, exhibits nontrivial scaling in its thermodynamic properties, and an associated nontrivial dynamical critical exponent. In the present work, we analytically compute low energy correlation functions in the background of the charged magnetic brane solution to 4+1-dimensional Einstein-Maxwell-Cher…
We consider dS_2/CFT_1 where the asymptotic symmetry group of the de Sitter spacetime contains the Virasoro algebra. We construct representations of the Virasoro algebra realized in the Fock space of a massive scalar field in de Sitter, built as excitations of the Euclidean vacuum state. These representations are unitary, without highest weight, and have vanishing central charge. They provide a prototype for a new class of conformal field theories dual to de Sitter backgrounds in string theory. The mapping of operators in the CFT to bulk quantities is described in detail. We comment on the ext…
We propose a systematic treatment of symmetries of KP integrable systems, including constrained (reduced) KP models ${\sl cKP}_{R,M}$, and their multi-component (matrix) generalizations. Any such integrable hierarchy is shown to possess an additional $({\hat U}(1)\oplus{\hat {SL}}(M))_{+} \oplus ({\hat {SL}}(M+R))_{-}$ loop-algebra symmetry. Also we provide a systematic construction of the full algebra of Virasoro additional symmetries in the case of constrained KP models which requires a nontrivial modification of the known Orlov-Schulman construction for the general unconstrained KP hierarch…
Resummation of Multi-Stress Tensors in Higher Dimensions
本文研究了全息共形场论中多重应力张量偏微分方程的精确解，通过重求和发现 d=2 下关联子可用 Bessel 函数表示并得到 Virasoro 真空块，而 d=4 下重求和会导致本质奇点，并证明了关联子可通过特定模式重建。
The asymptotics of characters $χ_{kλ}(\exp(h/k))$ of irreducible representations of a compact Lie group $G$ for large values of the scaling factor $k$ are given by Duistermaat-Heckman (DH) integrals over coadjoint orbits of $G$. This phenomenon generalises to coadjoint orbits of central extensions of loop groups $\widehat{LG}$ and of diffeomorphisms of the circle $\widehat{\rm Diff}(S^1)$. We show that the asymptotics of characters of integrable modules of affine Kac-Moody algebras and of the Virasoro algebra factorize into a divergent contribution of the standard form and a convergent contrib…
We consider the conformal $A_{n}$ Toda theory in AdS$_{2}$. Due to the bulk full Virasoro symmetry, this system provides an instance of a non-gravitational $\text{AdS}_{2}$/$\text{CFT}_{1}$ correspondence where the 1d boundary theory enjoys enhanced "$\frac{1}{2}$-Virasoro" symmetry. General boundary correlators are expected to be captured by the restriction of chiral correlators in a suitable $\mathcal WA_{n}$ Virasoro extension. At next-to-leading order in weak coupling expansion they have been conjectured to match the subleading terms in the large central charge expansion of the dual $\math…
Using the holographic machinery built up in a previous work, we show that the hidden SL(2,R) symmetry of a scalar quantum field propagating in a Rindler spacetime admits an enlargement in terms of a unitary positive-energy representation of Virasoro algebra, with central charge c=1, defined in the Fock representation. The Virasoro algebra of operators gets a manifest geometrical meaning if referring to the holographically associated QFT on the horizon: It is nothing but a representation of the algebra of vector fields defined on the horizon equipped with a point at infinity. All that happens p…
Finite Gauss-Sum Modular Kernels: Scalar Gap and a Pure AdS$_3$ Gravity No-Go Theorem
本文通过构建有限支持的窗口函数，推导了标量间隙的严格解析界限，并证明了纯AdS₃引力不存在单位ary CFT 的初级间隙高于Δ_{BTZ}。
Two types of new Chern-Simons (CS) densities, both defined in all odd and even dimensions, are proposed. These new CS densities feature a scalar field interacting with a scalar. In one case this is a Higgs scalar while in the other it is a Skyrme scalar. The motivation is to study the effects of adding these new CS terms to a Lagrangian which supports static soliton solutions prior to their introduction.
The vacuum expectation value of the surface energy-momentum tensor is evaluated for a scalar field obeying Robin boundary condition on a spherical brane in (D+1)-dimensional spacetime $Ri\times S^{D-1}$, where $Ri$ is a two-dimensional Rindler spacetime. The generalized zeta function technique is used in combination with the contour integral representation. The surface energies on separate sides of the brane contain pole and finite contributions. Analytic expressions for both these contributions are derived. For an infinitely thin brane in odd spatial dimensions, the pole parts cancel and the …
We study a model of free massless scalar fields on a two dimensional cylinder with metric that admits a change of signature between Lorentzian and Euclidean type (ET), across the two timelike hypersurfaces (with respect to Lorentzian region). Considering a long strip-shaped region of the cylinder, denoted by an angle θ, as the signature changed region it is shown that the energy spectrum depends on the angle θand in a sense differs from ordinary one for low energies. Morever diffeomorphism algebra of corresponding infinite conserved charges is different from '' Virasoro'' algebra and approache…
In this paper, we calculate the stress-energy tensor for a quantized massless conformally coupled scalar field in the background of a conformally flat brane-world geometries, where the scalar field satisfying Robin boundary conditions on two parallel plates. In the general case of Robin boundary conditions formula are derived for the vacuum expectation values of the energy-momentum tensor. Further the surface energy per unit area are obtained . As an application of the general formula we have considered the important special case of the AdS$_{4+1}$ bulk, moreover application to the Randall-Sun…
For a massive scalar field with general curvature coupling parameter we evaluate Wightman function, vacuum expectation values of the field square and the energy-momentum tensor induced by a $Z_{2}$-symmetric brane with finite thickness located on $(D+1)$-dimensional AdS bulk. For the general case of static plane symmetric interior structure the expectation values in the region outside the brane are presented as the sum of free AdS and brane induced parts. For a conformally coupled massless scalar the brane induced part in the vacuum energy-momentum tensor vanishes. In the limit of strong gravi…
Wightman function, the vacuum expectation values of the field square and the energy-momentum tensor are investigated for a massive scalar field with general curvature coupling parameter inside a wedge with two coaxial cylindrical boundaries. It is assumed that the field obeys Dirichlet boundary condition on bounding surfaces. The application of a variant of the generalized Abel-Plana formula enables to extract from the expectation values the contribution corresponding to the geometry of a wedge with a single shell and to present the interference part in terms of exponentially convergent integr…
Lovelock terms are polynomial scalar densities in the Riemann curvature tensor that have the remarkable property that their Euler-Lagrange derivatives contain derivatives of the metric of order not higher than two (while generic polynomial scalar densities lead to Euler-Lagrange derivatives with derivatives of the metric of order four). A characteristic feature of Lovelock terms is that their first nonvanishing term in the expansion of the metric around flat space is a total derivative. In this paper, we investigate generalized Lovelock terms defined as polynomial scalar densities in the Riema…
We present a full characterization of the phase transition in U(1) scalar field theory and of the associated vortex string thermodynamics in 3D. We show that phase transitions in the string densities exist and measure their critical exponents, both for the long string and the short loops. Evidence for a natural separation between these two string populations is presented. In particular our results strongly indicate that an infinite string population will only exist above the critical temperature. Canonical initial conditions for cosmic string evolution are show to correspond to the infinite te…
Wightman function, the vacuum expectation values of the field square and the energy-momentum tensor are investigated for a massive scalar field with general curvature coupling parameter in the region between two coaxial cylindrical boundaries. It is assumed that the field obeys general Robin boundary conditions on bounding surfaces. The application of a variant of the generalized Abel-Plana formula allows to extract from the expectation values the contribution from single shells and to present the interference part in terms of exponentially convergent integrals. The vacuum forces acting on the…
Whightman function, vacuum expectation values of the field square, and the energy-momentum tensor are investigated for a scalar field inside a wedge with and without a coaxial cylindrical boundary. Dirichlet boundary conditions are assumed on the bounding surfaces. The vacuum energy-momentum tensor is evaluated in the general case of the curvature coupling parameter. Making use of a variant of the generalized Abel-Plana formula, expectation values are presented as the sum of two terms. The first one corresponds to the geometry without a cylindrical boundary and the second one is induced by the…
Topological densities in Einstein-scalar-Gauss-Bonnet gravity
本工作研究了最大对称时空中Einstein-Gauss-Bonnet引力标量场的动力学演化，建立了依赖黄金比例的拓扑质量谱，发现其拓扑密度在Schwarzschild极限下对应标准模型辐射能量密度，并给出了质量随时间演化的损失率。
We consider the zero-point field fluctuations, and the related field energy densities, inside a one-dimensional and a three-dimensional cavity with a mobile wall. The mechanical degrees of freedom of the mobile wall are described quantum mechanically and they are fully included in the overall system dynamics. In this optomechanical system, the field and the wall can interact with each other through the radiation pressure on the wall, given by the photons inside the cavity or even by vacuum fluctuations. We consider two cases: the one-dimensional electromagnetic field and the three-dimensional …
We discuss a method of calculating the various scalar densities encountered in Lovelock theory which relies on diagrammatic, instead of algebraic manipulations. Taking advantage of the known symmetric and antisymmetric properties of the Riemann tensor which appears in the Lovelock densities, we map every quadratic or higher contraction into a corresponding permutation diagram. The derivation of the explicit form of each density is then reduced to identifying the distinct diagrams, from which we can also read off the overall combinatoric factors. The method is applied to the first Lovelock dens…
We analyze the Casimir densities and forces associated with a massive scalar quantum field confined between two parallel plates in a D-dimensional cosmic string spacetime. The plates are placed orthogonal to the string and the field obeys the Robin boundary conditions on them. The boundary-induced contributions are explicitly extracted in the vacuum expectation values (VEVs) of the field squared and energy-momentum tensor for both single and two plates. The VEV of the energy-momentum tensor, in additional to the diagonal components, contains an off-diagonal component corresponding to the shear…
Scalar vacuum densities on Beltrami pseudosphere
研究了标量场在贝尔特拉米伪球面上的真空密度特性，分析了曲率和拓扑对真空期望值的影响，发现应力随径向坐标变化显著。
We evaluate the positive-frequency Wightman function, the vacuum expectation values (VEVs) of the field squared and the energy-momentum tensor for a massive scalar field with general curvature coupling for a cylindrical shell in background of dS spacetime. The field is prepared in the Bunch-Davies vacuum state and on the shell the corresponding operator obeys Robin boundary condition. In the region inside the shell and for non-Neumann boundary conditions, the Bunch-Davies vacuum is a physically realizable state for all values of the mass and curvature coupling parameter. For both interior and …
The vacuum expectation values of the field squared and the energy-momentum tensor are investigated for a scalar field with Dirichlet boundary conditions and for the electromagnetic field inside a wedge with a coaxial cylindrical boundary. In the case of the electromagnetic field perfectly conducting boundary conditions are assumed on the bounding surfaces. By using the Abel-Plana-type formula for the series over the zeros of the Bessel function, the vacuum expectation values are presented in the form of the sum of two terms. The first one corresponds to the geometry without a cylindrical bound…
We present new results involving general higher-curvature gravities in three dimensions. The most general Lagrangian can be written as a function of the Ricci scalar $R$, $\mathcal{S}_2\equiv \tilde R_{a}^b \tilde R_b^a$ and $\mathcal{S}_3\equiv \tilde R_a^b \tilde R_b^c \tilde R_c^a$ where $\tilde R_{ab}$ is the traceless part of the Ricci tensor. First, we provide a formula for the exact number of independent order-$n$ densities, $\#(n)$. This satisfies the identity $\#(n-6)=\#(n)-n$. Then, we show that, linearized around a general Einstein solution, a generic order-$n\geq 2$ density can be …
We evaluate the Hadamard function and the vacuum expectation value (VEV) of the current density for a charged scalar field, induced by flat boundaries in spacetimes with an arbitrary number of toroidally compactified spatial dimensions. The field operator obeys the Robin conditions on the boundaries and quasiperiodicity conditions with general phases along compact dimensions. In addition, the presence of a constant gauge field is assumed. The latter induces Aharonov-Bohm-type effect on the VEVs. There is a region in the space of the parameters in Robin boundary conditions where the vacuum stat…
Positive frequency Wightman function and vacuum expectation value of the energy-momentum tensor are computed for a massive scalar field with general curvature coupling parameter subject to Robin boundary conditions on two parallel plates located on $D+1$ - dimensional AdS background. The general case of different Robin coefficients on separate plates is considered. The mode summation method is used with a combination of a variant of the generalized Abel-Plana formula for the series over zeros of combinations of cylinder functions. This allows us to extract manifestly the parts due to the AdS s…
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