A Note on Circle Compactification of Tensile Ambitwistor String

We discuss a number of problems associated with the circle compactification of the bosonic tensile ambitwistor string with the asymmetric vacuum choice. By considering the spectrum and physical state conditions, we show that the circle radius plays a role as a tuning parameter which determines the low energy effective field theory. At the self dual point, we construct the current operators and compute OPEs between them. While the final outcome remains as yet inconclusive, several new results are obtained. Through the current algebra analysis we show that there is a subsector of the massless states where the gauge symmetry is enhanced to $ISO(2)_L\times SU(2)_R$. Using the fact that the one loop partition function is not modular invariant, we show that tensile ambitwistor string partition function is exactly the same as a field theory partition function. Our result proves that despite the existence of winding modes, which is a typical characteristic of a string, the tensile ambitwistor string behaves as a point particle theory.Comment: 31 pages, v2: minor corrections, reference added, published in Nucl.Phys.

Can the cosmological constant undergo abrupt changes?

The existence of a simple spherically symmetric and static solution of the Einstein equations in the presence of a cosmological constant vanishing outside a definite value of the radial distance is investigated. A particular succession of field configurations, which are solutions of the Einstein equations in the presence of the considered cosmological term and auxiliary external sources, is constructed. Then, it is shown that the associated succession of external sources tend to zero in the sense of the generalized functions. The type of weak solution that is found becomes the deSitter homogeneous space-time for the interior region, and the Schwartzschild space in the outside zone.Comment: 10 pages, 1 figur

Spontaneous Symmetry Breaking in Tensor Theories

In this work we study spontaneous symmetry breaking patterns in tensor models. We focus on the patterns which lead to effective matrix theories transforming in the adjoint of $U(N)$. We find the explicit form of the Goldstone bosons which are organized as matrix multiplets in the effective theory. The choice of these symmetry breaking patterns is motivated by the fact that, in some contexts, matrix theories are dual to gravity theories. Based on this, we aim to build a bridge between tensor theories, quantum gravity and holography.Comment: 40 pp, 1 fig. Update to match the published versio

The gauge structure of Exceptional Field Theories and the tensor hierarchy

We address the construction of manifest U-duality invariant generalized diffeomorphisms. The closure of the algebra requires an extension of the tangent space to include a tensor hierarchy indicating the existence of an underlying unifying structure, compatible with E_{11} and Borcherds algebras constructions. We begin with four-dimensional gauged maximal supergravity, and build a generalized Lie derivative that encodes all the gauge transformations of the theory. A generalized frame is introduced, which accommodates for all the degrees of freedom, including the tensor hierarchy. The generalized Lie derivative defines generalized field-dependent fluxes containing all the covariant quantities in the theory, and the closure conditions give rise to their corresponding Bianchi Identities. We then move towards the construction of a full generalized Lie derivative defined on an extended space, analyze the closure conditions, and explore the connection with that of maximal gauged supergravity via a generalized Scherk-Schwarz reduction, and with 11-dimensional supergravity.Comment: 53 page

Extended geometry and gauged maximal supergravity

We consider generalized diffeomorphisms on an extended mega-space associated to the U-duality group of gauged maximal supergravity in four dimensions, E_7. Through the bein for the extended metric we derive dynamical (field-dependent) fluxes taking values in the representations allowed by supersymmetry, and obtain their quadratic constraints from gauge consistency conditions. A covariant generalized Ricci tensor is introduced, defined in terms of a connection for the generalized diffeomorphisms. We show that for any torsionless and metric-compatible generalized connection, the Ricci scalar reproduces the scalar potential of gauged maximal supergravity. We comment on how these results extend to other groups and dimensions.Comment: 41 pages. v2,v3: minor changes and references adde

Remarks on entanglement entropy for gauge fields

In gauge theories the presence of constraints can obstruct expressing the global Hilbert space as a tensor product of the Hilbert spaces corresponding to degrees of freedom localized in complementary regions. In algebraic terms, this is due to the presence of a center --- a set of operators which commute with all others --- in the gauge invariant operator algebra corresponding to finite region. A unique entropy can be assigned to algebras with center, giving place to a local entropy in lattice gauge theories. However, ambiguities arise on the correspondence between algebras and regions. In particular, it is always possible to choose (in many different ways) local algebras with trivial center, and hence a genuine entanglement entropy, for any region. These choices are in correspondence with maximal trees of links on the boundary, which can be interpreted as partial gauge fixings. This interpretation entails a gauge fixing dependence of the entanglement entropy. In the continuum limit however, ambiguities in the entropy are given by terms local on the boundary of the region, in such a way relative entropy and mutual information are finite, universal, and gauge independent quantities.Comment: 26 pages, 7 figure

A String Theory Which Isn't About Strings

Quantization of closed string proceeds with a suitable choice of worldsheet vacuum. A priori, the vacuum may be chosen independently for left-moving and right-moving sectors. We construct {\sl ab initio} quantized bosonic string theory with left-right asymmetric worldsheet vacuum and explore its consequences and implications. We critically examine the validity of new vacuum and carry out first-quantization using standard operator formalism. Remarkably, the string spectrum consists only of a finite number of degrees of freedom: string gravity (massless spin-two, Kalb-Ramond and dilaton fields) and two massive spin-two Fierz-Pauli fields. The massive spin-two fields have negative norm, opposite mass-squared, and provides a Lee-Wick type extension of string gravity. We compute two physical observables: tree-level scattering amplitudes and one-loop cosmological constant. Scattering amplitude of four dilatons is shown to be a rational function of kinematic invariants, and in $D=26$ factorizes into contributions of massless spin-two and a pair of massive spin-two fields. The string one loop partition function is shown to perfectly agree with one loop Feynman diagram of string gravity and two massive spin-two fields. In particular, it does not exhibit modular invariance. We critically compare our construction with recent studies and contrast differences.Comment: 42 pages, 1 figure, minor corrections, references added; v3: minor corrections, references added, published version in JHE