Two-form Potential Research Articles

Bochner formulas, functional inequalities and generalized Ricci flow

As a consequence of the Bochner formula for the Bismut connection acting on gradients, we show sharp universal Poincaré and log-Sobolev inequalities along solutions to generalized Ricci flow. Using the two-form potential we define a twisted connection on spacetime which determines an adapted Brownian motion on the frame bundle, yielding an adapted Malliavin gradient on path space. We show a Bochner formula for this operator, leading to characterizations of generalized Ricci flow in terms of universal Poincaré and log-Sobolev type inequalities for the associated Malliavin gradient and Ornstein-Uhlenbeck operator.

Existence of Harmonic Maps with Two-Form and Scalar Potentials

In this paper, we obtain existence results of Dirichlet problem for harmonic maps with two-form and scalar potentials from Riemannian surfaces M with nonempty boundary into compact manifolds N with convex boundary and complete manifolds N via the heat flow method.

Classifying solutions to Romans supergravity with a zero B-field

Expanding on previous papers, we continue studying Euclidean Romans supergravity in six dimensions with a non-trivial Abelian R-symmetry gauge field. Using a set of differential constraints on a SU(2) structure, we look for further geometric solutions to such equations when we turn off the two-form potential B. We find that the six-dimensional space is described by a two-dimensional fibration over a four-dimensional manifold with a Kähler metric. We then classify these types of solutions.

On the full bosonic string from Minkowski space to Riemannian manifolds

We study the action of the full bosonic string for the domain being two-dimensional Minkowski space and the target a Riemannian manifold. Its critical points couple the wave map equation to a scalar and a two-form potential. Besides investigating their basic features we establish existence results for the latter.

Static cosmic strings in space–time with torsion, and strings with electromagnetism

Cosmic strings are considered in space–time with torsion derived from a two-form potential, and in Minkowski space–time with electromagnetism. Using the curvature scalar as the geometrical part of the Lagrangian density, and the natural coupling to strings, the field equations are derived. It is shown a static string loop may satisfy the string equations of motion in the presence of an external torsion field. The gravitational field of the static string are derived in the weak field limit, and it is shown the gravitational field is repulsive exterior to the string. In Minkowski space–time, it is shown an external magnetic field can also give rise to a static loop.

The heat flow for the full bosonic string.

We study harmonic maps from surfaces coupled to a scalar and a two-form potential, which arise as critical points of the action of the full bosonic string. We investigate several analytic and geometric properties of these maps and prove an existence result by the heat-flow method.

Fermionic and bosonic mass deformations of N $$ \mathcal{N} $$ = 4 SYM and their bulk supergravity dual

We examine the AdS-CFT dual of arbitrary (non)supersymmetric fermionic mass deformations of $$ \mathcal{N} $$ = 4 SYM, and investigate how the backreaction of the RR and NS-NS two-form potentials dual to the fermion masses contribute to Coulomb-branch potential of D3 branes, which we interpret as the bulk boson mass matrix. Using representation theory and supergravity arguments we show that the fermion masses completely determine the trace of this matrix, and that on the other hand its traceless components have to be turned on as non-normalizable modes. Our result resolves the tension between the belief that the AdS bulk dual of the trace of the boson mass matrix (which is not a chiral operator) is a stringy excitation with dimension of order (g s N )1/4 and the existence of non-stringy supergravity flows describing theories where this trace is nonzero, by showing that the stringy mode does not parameterize the sum of the squares of the boson masses but rather its departure from the trace of the square of the fermion mass matrix. Hence, asymptotically-AdS flows can only describe holographically theories where the sums of the squares of the bosonic and fermionic masses are equal, which is consistent with the weakly-coupled result that only such theories can have a conformal UV fixed point.

Mass and angular momentum of black holes in low-energy heterotic string theory

We investigate conserved charges in the low-energy effective field theory describing heterotic string theory. Starting with a general Lagrangian that consists of a metric, a scalar field, a vector gauge field, together with a two-form potential, we derive off-shell Noether potentials of the Lagrangian and generalize the Abbott–Deser–Tekin (ADT) formalism to the off-shell level by establishing one-to-one correspondence between the ADT potential and the off-shell Noether potential. It is proved that the off-shell generalized ADT formalism is conformally invariant. Then, we apply the formulation to compute mass and angular momentum of the four-dimensional Kerr–Sen black hole and the five-dimensional rotating charged black string in the string frame without a necessity to transform the metrics into the Einstein frame.

The powers of monodromy

Flux couplings to string theory axions yield super-Planckian field ranges along which the axion potential energy grows. At the same time, other aspects of the physics remain essentially unchanged along these large displacements, respecting a discrete shift symmetry with a sub-Planckian period. After a general overview of this monodromy effect and its application to large-field inflation, we present new classes of specific models of monodromy inflation, with monomial potentials μ 4−p ϕ p . A key simplification in these models is that the inflaton potential energy plays a leading role in moduli stabilization during inflation. The resulting inflaton-dependent shifts in the moduli fields lead to an effective flattening of the inflaton potential, i.e. a reduction of the exponent from a fiducial value p 0 to p < p 0. We focus on examples arising in compactifications of type IIB string theory on products of tori or Riemann surfaces, where the inflaton descends from the NS-NS two-form potential B 2, with monodromy induced by a coupling to the R-R field strength F 1. In this setting we exhibit models with p = 2/3, 4/3, 2, and 3, corresponding to predictions for the tensor-to-scalar ratio of r ≈ 0.04, 0.09, 0.13, and 0.2, respectively. Using mirror symmetry, we also motivate a second class of examples with the role of the axions played by the real parts of complex structure moduli, with fluxes inducing monodromy.

P-wave holographic superconductors and five-dimensional gauged supergravity

We explore five-dimensional ${\cal N}=4$ $SU(2)\times U(1)$ and ${\cal N}=8$ SO(6) gauged supergravities as frameworks for condensed matter applications. These theories contain charged (dilatonic) black holes and 2-forms which have non-trivial quantum numbers with respect to U(1) subgroups of SO(6). A question of interest is whether they also contain black holes with two-form hair with the required asymptotic to give rise to holographic superconductivity. We first consider the ${\cal N}=4$ case, which contains a complex two-form potential $A_{\mu\nu}$ which has U(1) charge $\pm 1$. We find that a slight generalization, where the two-form potential has an arbitrary charge $q$, leads to a five-dimensional model that exhibits second-order superconducting transitions of p-wave type where the role of order parameter is played by $A_{\mu\nu}$, provided $q \gtrsim 5.6$. We identify the operator that condenses in the dual CFT, which is closely related to ${\cal N}=4$ Super Yang-Mills theory with chemical potentials. Similar phase transitions between R-charged black holes and black holes with 2-form hair are found in a generalized version of the ${\cal N}=8$ gauged supergravity Lagrangian where the two-forms have charge $q\gtrsim 1.8$.

Enthalpy and the mechanics of AdS black holes

We present geometric derivations of the Smarr formula for static AdS black holes and an expanded first law that includes variations in the cosmological constant. These two results are further related by a scaling argument based on Euler's theorem. The key new ingredient in the constructions is a two-form potential for the static Killing field. Surface integrals of the Killing potential determine the coefficient of the variation of Λ in the first law. This coefficient is proportional to a finite, effective volume for the region outside the AdS black hole horizon, which can also be interpreted as minus the volume excluded from a spatial slice by the black hole horizon. This effective volume also contributes to the Smarr formula. Since Λ is naturally thought of as a pressure, the new term in the first law has the form of effective volume times change in pressure that arises in the variation of the enthalpy in classical thermodynamics. This and related arguments suggest that the mass of an AdS black hole should be interpreted as the enthalpy of the spacetime.

General perturbations for braneworld compactifications and the six dimensional case

Our main objective is to study how braneworld models of higher codimension differ from the 5D case and traditional Kaluza-Klein compactifications. We first derive the classical dynamics describing the physical fluctuations in a wide class of models incorporating gravity, non-Abelian gauge fields, the dilaton and two-form potential, as well as 3-brane sources. Next, we use these results to study braneworld compactifications in 6D supergravity, focusing on the bosonic fields in the minimal model; composed of the supergravity-tensor multiplet and the U(1) gauge multiplet whose flux supports the compactification. For unwarped models sourced by positive tension branes, a harmonic analysis allows us to solve the large, coupled, differential system completely and obtain the full 4D spin-2,1 and 0 particle spectra, establishing (marginal) stability and a qualitative behaviour similar to the smooth sphere compactification. We also find interesting results for models with negative tension branes; extra massless Kaluza-Klein vector fields can appear in the spectra, beyond those expected from the isometries in the internal space. These fields imply an enhanced gauge symmetry in the low energy 4D effective theory obtained by truncating to the massless sector, which is explicitly broken as higher modes are excited, until the full 6D symmetries are restored far above the Kaluza-Klein scale. Remarkably, the low energy effective theory does not seem to distinguish between a compactification on a smooth sphere and these singular, deformed spheres.

The gaugings of maximalD= 6 supergravity

We construct the most general gaugings of the maximal D=6 supergravity. The theory is (2,2) supersymmetric, and possesses an on-shell SO(5,5) duality symmetry which plays a key role in determining its couplings. The field content includes 16 vector fields that carry a chiral spinor representation of the duality group. We utilize the embedding tensor method which determines the appropriate combinations of these vectors that participate in gauging of a suitable subgroup of SO(5,5). The construction also introduces the magnetic duals of the 5 two-form potentials and 16 vector fields.

Rotating Circular Strings, and Infinite Non-Uniqueness of Black Rings

We present new self-gravitating solutions in five dimensions that describe circular strings, i.e., rings, electrically coupled to a two-form potential (as e.g., fundamental strings do), or to a dual magnetic one-form. The rings are prevented from collapsing by rotation, and they create a field analogous to a dipole, with no net charge measured at infinity. They can have a regular horizon, and we show that this implies the existence of an infinite number of black rings, labeled by a continuous parameter, with the same mass and angular momentum as neutral black rings and black holes. We also discuss the solution for a rotating loop of fundamental string. We show how more general rings arise from intersections of branes with a regular horizon (even at extremality), closely related to the configurations that yield the four-dimensional black hole with four charges. We reproduce the Bekenstein-Hawking entropy of a large extremal ring through a microscopic calculation. Finally, we discuss some qualitative ideas for a microscopic understanding of neutral and dipole black rings.

Various faces of type IIA supergravity

We derive a duality-symmetric action for type IIA D=10 supergravity by the Kaluza–Klein dimensional reduction of the duality-symmetric action for D=11 supergravity with the 3-form and 6-form gauge field. We then double the bosonic fields arising as a result of the Kaluza–Klein dimensional reduction and add mass terms to embrace the Romans's version, so that in its final form the bosonic part of the action contains the dilaton, NS–NS and RR potentials of the standard type IIA supergravity as well as their duals, the corresponding duality relations are deduced directly from the action. We discuss the relation of our approach to the doubled field formalism by Cremmer, Julia, Lü and Pope, complete the extension of this construction to the supersymmetric case and lift it onto the level of the proper duality-symmetric action. We also find a new dual formulation of type IIA D=10 supergravity in which the NS–NS two-form potential is replaced with its six-form counterpart. A truncation of this dual model produces the Chamseddine's version of N=1, D=10 supergravity.

Non-commutativity in a time-dependent background

We compute a time-dependent non-commutativity parameter in a model with a time-dependent background, a spacetime metric of the plane wave type supported by a Neveu–Schwarz two-form potential. This model is the open string version of the WZW model based on a non-semi-simple group previously studied by Nappi and Witten. Like its closed string counterpart, it is exactly conformally invariant to all orders in α′. We quantize the sigma-model in light-cone gauge, compute the worldsheet propagator, and use it to derive the non-commutativity parameter.

GAUGE TRANSFORMATIONS OF THE NON-ABELIAN TWO-FORM

A novel inhomogeneous gauge transformation law is proposed for a non-Abelian adjoint two-form potential in four dimensions. Rules for constructing actions invariant under this are given. The auxiliary vector field which appears in some of these theories transforms like a second connection. Some of the actions also show a local symmetry which is not generated by any local constraint, a novelty for classical field theories. Both types of symmetries change the action by total divergences, suggesting that boundary degrees of freedom have to be taken into account for local quantization.

Neveu-Schwarz 5-branes in type-IIA supergravity and gravitational anomalies

We construct a gravitational-anomaly-free effective action for the coupled system of type-IIA $D=10$ dynamical supergravity interacting with a NS5-brane. The NS5-brane is considered as elementary in that the associated current is a $\ensuremath{\delta}$ function supported on its world volume. Our approach is based on a Chern kernel which encodes the singularities of the three-form field strength near the brane in an SO(4)-invariant way and provides a solution for its Bianchi identity in terms of a two-form potential. A dimensional reduction of the recently constructed anomaly-free effective action for an elementary M5-brane in $D=11$ is seen to reproduce our ten-dimensional action. The Chern-kernel approach provides in particular a concrete realization of the anomaly cancellation mechanism envisaged by Witten.

DUALITY PROPERTIES OF SUPER D-BRANE ACTIONS IN GENERAL TYPE IIB SUPERGRAVITY BACKGROUND

We examine duality transformations of supersymmetric and κ-symmetric Dp-brane actions in a general type IIB supergravity background where in particular the dilaton and the axion are not supposed to be zero or a constant but a general superfield. Due to nonconstant dilaton and axion, we can explicitly show that the dilaton and the axion as well as the two two-form gauge potentials transform as doublets under the SL (2,R) transformation from the point of view of the world volume field theory.

INTERACTING SIX-DIMENSIONAL TOPOLOGICAL FIELD THEORIES

We study the gauge-fixing and symmetries (BRST-invariance and vector supersymmetry) of various six-dimensional topological models involving Abelian or non-Abelian two-form potentials.