Kalb-Ramond Research Articles

String theory and string Newton–Cartan geometry**Dedicated to the memory of P G O Freund.

Nonrelativistic string theory is described by a sigma model with a relativistic worldsheet and a nonrelativistic target spacetime geometry, that is called string Newton–Cartan geometry. In this paper we obtain string Newton–Cartan geometry as a limit of the Riemannian geometry of general relativity with a fluxless two-form field. We then apply the same limit to relativistic string theory in curved background fields and show that it leads to nonrelativistic string theory in a string Newton–Cartan geometry coupled to a Kalb–Ramond and dilaton field background. Finally, we use our limiting procedure to study the spacetime equations of motion and the T-duality transformations of nonrelativistic string theory. Our results reproduce the recent studies of beta-functions and T-duality of nonrelativistic string theory obtained from the microscopic worldsheet definition of nonrelativistic string theory.

Relating non-relativistic string theories

Non-relativistic string theories promise to provide simpler theories of quantum gravity as well as tractable limits of the AdS/CFT correspondence. However, several apparently distinct non-relativistic string theories have been constructed. In particular, one approach is to reduce a relativistic string along a null isometry in target space. Another method is to perform an appropriate large speed of light expansion of a relativistic string. Both of the resulting non-relativistic string theories only have a well-defined spectrum if they have nonzero winding along a longitudinal spatial direction. In the presence of a Kalb-Ramond field, we show that these theories are equivalent provided the latter direction is an isometry. Finally, we consider a further limit of non-relativistic string theory that has proven useful in the context of AdS/CFT (related to Spin Matrix Theory). In that case, the worldsheet theory itself becomes non-relativistic and the dilaton coupling vanishes.

Emergent Kalb-Ramond fields from a dimer model

The emergence of a Kalb-Ramond field and string charge in the lattice is discussed. The local bosonic model with rotor variables placed on the faces of a cubic lattice is considered. The coupling model consisting of the Maxwell fields and the Kalb-Ramond field is given. This construction naturally incorporates the emerging coupling between both gauge and string fields. In the process, an object that resembles to a D-brane on the lattice is introduced.

Holographic correspondence of F(R) gravity with/without matter fields

In this paper, we apply the holographic principle to the early universe, obtaining an inflation realization of holographic origin. First we show that under the consideration of extended infrared cutoffs, there exists a holographic correspondence of various F(R) (such as quadratic, cubic, exponential F(R) models) cosmological models in the absence of matter fields. Then we establish that such holographic correspondence is not only confined to the vacuum F(R) gravity but also can be extended to the higher curvature models along with matter fields. In the presence of matter field, in particular the second-rank antisymmetric Kalb-Ramond field, all the considered F(R) models lead to a viable inflationary phenomenology consistent with Planck 2018 constraints. We further extend our discussion of holographic correspondence to F(T) cosmological models.

Proposal for a New Quantum Theory of Gravity

Abstract We recall a classical theory of torsion gravity with an asymmetric metric, sourced by a Nambu–Goto + Kalb–Ramond string [R. T. Hammond, Rep. Prog. Phys. 65, 599 (2002)]. We explain why this is a significant gravitational theory and in what sense classical general relativity is an approximation to it. We propose that a noncommutative generalisation of this theory (in the sense of Connes’ noncommutative geometry and Adler’s trace dynamics) is a “quantum theory of gravity.” The theory is in fact a classical matrix dynamics with only two fundamental constants – the square of the Planck length and the speed of light, along with the two string tensions as parameters. The guiding symmetry principle is that the theory should be covariant under general coordinate transformations of noncommuting coordinates. The action for this noncommutative torsion gravity can be elegantly expressed as an invariant area integral and represents an atom of space–time–matter. The statistical thermodynamics of a large number of such atoms yields the laws of quantum gravity and quantum field theory, at thermodynamic equilibrium. Spontaneous localisation caused by large fluctuations away from equilibrium is responsible for the emergence of classical space–time and the field equations of classical general relativity. The resolution of the quantum measurement problem by spontaneous collapse is an inevitable consequence of this process. Quantum theory and general relativity are both seen as emergent phenomena, resulting from coarse graining of the underlying noncommutative geometry. We explain the profound role played by entanglement in this theory: entanglement describes interaction between the atoms of space–time–matter, and indeed entanglement appears to be more fundamental than quantum theory or space–time. We also comment on possible implications for black hole entropy and evaporation and for cosmology. We list the intermediate mathematical analysis that remains to be done to complete this programme.

CFT6 bulk/boundary correspondence and emergent gravity

We revisit a non-perturbative formulation of quantum gravity in 1.5 order underlying an emergent gravitational pair of -brane with a renewed interest. In particular, the formulation is governed by a geometric torsion in second order with an on-shell Neveu–Schwarz form in first order. Interestingly the gravitational pair is sourced by a Kalb–Ramond two form CFT on a D5-brane in d = 10 type IIB superstring theory. We show that a generic form theory containing a CFT sector in d = 6 bulk may be described by a boundary AdS5 with a quintessence Q. Analysis reveals that the bulk/boundary duality in emergent gravity can be a potential tool to explore the quintessential cosmology.

The shadow of dark matter as a shadow of string theory

We point out that string theory can solve the conundrum to explain the emergence of an electroweak dipole moment from electroweak singlets through induction of those dipole moments through a Kalb–Ramond dipole coupling. This can generate a U_Y(1) portal to dark matter and entails the possibility that the U_Y(1) gauge field is related to a fundamental vector field for open string interactions. The requirement to explain the observed dark matter abundance relates the coupling scale M in the corresponding low-energy effective U_Y(1) portal to the dark matter mass m_chi . The corresponding electron recoil cross sections for a single dipole coupled dark matter species are generically below the current limits from XENON, SuperCDMS and SENSEI, except in the GeV mass range if the electric dipole coupling becomes stronger than the magnetic coupling, a_e^2ge a_m^2. Furthermore, the recoil cross sections are above the neutrino floor, and the U_Y(1) portal can be tested with longer exposure or larger detectors. Discovery of electroweak dipole dark matter would therefore open an interesting window into string phenomenology.

Inflationary universe in F(R) gravity with antisymmetric tensor fields and their suppression during its evolution

The intriguing question, why the present scale of the universe is free from any perceptible footprints of rank-2 antisymmetric tensor fields? (generally known as Kalb-Ramond fields) is addressed. A quite natural explanation of this issue is given from the angle of higher-curvature gravity, both in four- and in five-dimensional spacetime. The results here obtained reveal that the amplitude of the Kalb-Ramond field may be actually large and play a significant role during the early universe, while the presence of higher-order gravity suppresses this field during the cosmological evolution, so that it eventually becomes negligible in the current universe. Besides the suppression of the Kalb-Ramond field, the extra degree of freedom in $F(R)$ gravity, usually known as scalaron, also turns out to be responsible for inflation. Such F(R) gravity with Kalb-Ramond fields may govern the early universe to undergo an inflationary stage at early times (with the subsequent graceful exit) for wider range of F(R) gravity than without antisymmetric fields.. Furthermore, the models---in four- and five-dimensional spacetimes---are linked to observational constraints, with the conclusion that the corresponding values of the spectral index and tensor-to-scalar ratio closely match the values provided by the Planck survey 2018 data.

Directly from H-flux to the family of three nonlocal R-flux theories

In this article we consider T-dualization of the 3D closed bosonic string in the weakly curved background — constant metric and Kalb-Ramond field with one nonzero component, Bxy = Hz, where field strength H is infinitesimal. We use standard and generalized Buscher T-dualization procedure and make T-dualization starting from coordinate z, via y and finally along x coordinate. All three theories are nonlocal, because variable ΔV, defined as line integral, appears as an argument of background fields. After the first T-dualization we obtain commutative and associative theory, while after we T-dualize along y, we get, κ-Minkowski-like, noncommutative and associative theory. At the end of this T-dualization chain we come to the theory which is both noncommutative and nonassociative. The form of the final T-dual action does not depend on the order of T-dualization while noncommutativity and nonassociativity relations could be obtained from those in the x → y → z case by replacing H → −H.

Effective action of a dynamical Dp-brane with background fluxes

We shall construct the Dirac-Born-Infeld like and the Wess–Zumino like actions for a dynamical Dp-brane with the U(1) gauge potential and the Kalb–Ramond background field. The brane dynamics simultaneously has both tangential and transverse components. Our calculations will be in the context of the type II superstring theory, via the boundary state formalism.

Outline for a Quantum Theory of Gravity

Abstract By invoking an asymmetric metric tensor, and borrowing ideas from non-commutative geometry, string theory, and trace dynamics, we propose an action function for quantum gravity. The action is proportional to the four-dimensional non-commutative curvature scalar (which is torsion dependent), which is sourced by the Nambu–Goto world-sheet action for a string plus the Kalb–Ramond string action. This ‘quantum gravity’ is actually a non-commutative classical matrix dynamics, and the only two fundamental constants in the theory are the square of the Planck length and the speed of light. By treating the entity described by this action as a microstate, one constructs the statistical thermodynamics of a large number of such microstates, in the spirit of trace dynamics. Quantum field theory (and ℏ) and quantum general relativity (and G) emerge from the underlying matrix dynamics in the thermodynamic limit. Statistical fluctuations, which are inevitably present about equilibrium, are the source for spontaneous localisation, which drives macroscopic quantum gravitational systems to the classical general relativistic limit. While the mathematical formalism governing these ideas remains to be developed, we hope to highlight here the deep connection between quantum foundations and the sought-for quantum theory of gravity. In the sense described in this article, ongoing experimental tests of spontaneous collapse theories are in fact also tests of string theory!

Logarithmic-corrected R2 gravity inflation in the presence of Kalb-Ramond fields

In this paper we shall study the inflationary aspects of a logarithmic corrected R2 Starobinsky inflation model, in the presence of a Kalb-Ramond field in the gravitational action of F(R) gravity. Our main interest is to pin down the effect of this rank two antisymmetric tensor field on the inflationary phenomenology of the F(R) gravity theory at hand. The effects of the Kalb-Ramond field are expected to be strong during the inflationary era, however as the Universe expands, the energy density of the Kalb-Ramond field scales as ∼ a−6 so dark matter and radiation dominate over the Kalb-Ramond field effects. In general, antisymmetric fields constitute the field content of superstring theories, and thus their effect at the low-energy limit of the theory is expected to be significant. As we will show, for a flat Friedmann-Robertson-Walker metric, the Kalb-Ramond field actually reduces to a scalar field, so it is feasible to calculate the observational indices of inflation. We shall calculate the spectral index and the tensor-to-scalar ratio for the model at hand, by assuming two conditions for the resulting Kalb-Ramond scalar field, the slow-roll and the constant-roll condition. As we shall demonstrate, in both the slow-roll and constant-roll cases, compatibility with the latest observational data can be achieved. Also the effect of the Kalb-Ramond field on the inflationary phenomenology is to increase the amount of the predicted primordial gravitational radiation, in comparison to the corresponding f(R) gravities, however the results are still compatible with the observational data.

The role of temperature dependent string-inspired CPT violating backgrounds in leptogenesis and the chiral magnetic effect

In a temperature dependent CPT-Violating (CPTV) axial time-like background (induced by the Kalb-Ramond tensor field of string theory) we discuss leptogenesis by solving the Boltzmann equation.The current work non-trivially modifies the framework of a previous phenomenological approach by the authors where the CPTV axial background was considered to be a constant (with no microscopic justification). The constant background approximation though is shown to capture the main phenomenological features of leptogenesis. On comparing our analysis to the related chiral magnetic effect for axial current condensates, we conclude that the Kalb-Ramond field does not play the role of the chiral chemical potential needed for that effect.

Modular constraints on superconformal field theories

We constrain the spectrum of mathcal{N} = (1, 1) and mathcal{N} = (2, 2) superconformal field theories in two-dimensions by requiring the NS-NS sector partition function to be invariant under the Γθ congruence subgroup of the full modular group SL(2, ℤ). We employ semi-definite programming to find constraints on the allowed spectrum of operators with or without U(1) charges. Especially, the upper bounds on the twist gap for the noncurrent primaries exhibit interesting peaks, kinks, and plateau. We identify a number of candidate rational (S)CFTs realized at the numerical boundaries and find that they are realized as the solutions to modular differential equations associated to Γθ. Some of the candidate theories have been discussed by Höhn in the context of self-dual extremal vertex operator (super)algebra. We also obtain bounds for the charged operators and study their implications to the weak gravity conjecture in AdS3.

Spontaneous CPT Violation and Quantum Anomalies in a Model for Matter–Antimatter Asymmetry in the Cosmos

We review scenarios of baryogenesis through leptogenesis at early epochs of the universe, in string-inspired minimal extensions of the Standard Model (SM), involving heavy right-handed Majorana neutrinos. Spontaneous violation of CPT symmetry is induced by appropriate (in general, temperature-dependent) backgrounds of the Kalb–Ramond (KR) axion field, which has its origins in the (bosonic) massless string multiplet. As interesting features of the model, we also discuss two issues associated with quantum (chiral) anomalies: (i) the non-contribution of the KR axion background to the (anomalous) chiral magnetic effect, which arises in the presence of external electromagnetic fields and non-zero chiral chemical potentials of charged fermions; and (ii) the potential role of quantum fluctuations of the KR axion on the (anomalous) radiative generation of a Majorana mass for the right-handed neutrinos themselves.

Antisymmetric tensor propagator with spontaneous Lorentz violation

In this work, we study the spontaneous Lorentz symmetry breaking due to an antisymmetric 2-tensor field in Minkowski spacetime. For a smooth quadratic potential, the spectrum of the theory exhibits massless and massive excitations. We show that the equations of motion for the free field obey some constraints which lead to the massive mode being nonpropagating at leading order. Besides, there exists a massless mode in the theory which can be identified with the usual Kalb-Ramond field, carrying only one on-shell degree of freedom. The same conclusion holds when one analyses the pole structure of its Feynman propagator. A new complete set of spin-type operators is found, which was the requirement to evaluate the propagator of the Kalb-Ramond field modified by the presence of a nonzero vacuum expectation value responsible for the Lorentz violation.

A broad pseudovector glueball from holographic QCD

We study the decay of a pseudovector glueball with quantum numbers JPC=1+−, the lightest glueball with spin different from zero or two, in the top–down holographic Witten–Sakai–Sugimoto model. This glueball is dual to the string-theoretic Kalb–Ramond tensor field, which completely fixes all its couplings by gauge invariance and D-brane anomaly inflow. The dominant decay channels are determined by a Chern–Simons-like action for the flavor branes; couplings from the Dirac–Born–Infeld action turn out to be subdominant. While the resulting width is parametrically of order Nc−2λ−1 for Nc colors and 't Hooft coupling λ, when extrapolated to Nc=3 and with λ matched to experimental data, the prediction is that the pseudovector glueball is an extremely broad resonance.

On brane curvature couplings from disk amplitude

The Chern–Simons coupling on D-branes in string theory is known to receive higher derivative corrections which include the curvature tensor and the Neveu–Schwarz B-field. We find some curvature couplings of D-branes to closed string fields by evaluating string theory disc amplitudes of one Ramond–Ramond field C(p+1) and two gravitons in the presence of a single Dp-brane in type II string theory.

Kerr-Schild double field theory and classical double copy

The Kerr-Schild (KS) formalism is a powerful tool for constructing exact solutions in general relativity. In this paper, we present a generalization of the conventional KS formalism to double field theory (DFT) and supergravities. We introduce a generalized KS ansatz for the generalized metric in terms of a pair of null vectors. Applying this ansatz to the equations of motion of DFT, we construct the generalized KS field equation. While the generalized KS equations are quadratic in the fields, we show that it is possible to find solutions by considering linear equations only. Furthermore, we construct a Killing spinor equation under the generalized KS ansatz. Based on this formalism, we show that the classical double copy structure, which represents solutions of the Einstein equation in terms of solutions of the Maxwell equation, can be extended to the entire massless string NS-NS sector. We propose a supersymmetric classical double copy which shows that solutions of the Killing spinor equation can be realized in terms of solutions of the BPS equation of the supersymmetric Maxwell theory.

Charged black strings and black branes in Lovelock theories

It is well known that the Reissner-Norstrom solution of Einstein-Maxwell theory cannot be cylindrically extended to higher dimension, as with the black hole solutions in vacuum. In this paper we show that this result is circumvented in Lovelock gravity. We prove that the theory containing only the quadratic Lovelock term, the Gauss-Bonnet term, minimally coupled to a $U(1)$ field, admits homogeneous black string and black brane solutions characterized by the mass, charge and volume of the flat directions. We also show that theories containing a single Lovelock term of order $n$ in the Lagrangian coupled to a $(p-1)$-form field admit simple oxidations only when $n$ equals $p$, giving rise to new, exact, charged black branes in higher curvature gravity. For General Relativity this stands for a Lagrangian containing the Einstein-Hilbert term coupled to a massless scalar field, and no-hair theorems in this case forbid the existence of black branes. In all these cases the field equations acquire an invariance under a global scaling scale transformation of the metric. As explicit examples we construct new magnetically charged black branes for cubic Lovelock theory coupled to a Kalb-Ramond field in dimensions $(3m+2)+q$, with $m$ and $q$ integers, and the latter denoting the number of extended flat directions. We also construct dyonic solutions in quartic Lovelock theory in dimension $(4m+2)+q$.