Bosonic Part Research Articles

Non-relativistic limits of bosonic and heterotic Double Field Theory

The known stringy non-relativistic (NR) limit of the universal NS-NS sector of supergravity has a finite Lagrangian due to non-trivial cancellations of divergent parts coming from the metric and the B-field. We demonstrate that in Double Field Theory (DFT) and generalised geometry these cancellations already happen at the level of the generalised metric, which is convergent in the limit c → ∞, implying that the NR limit can be imposed before solving the strong constraint. We present the c-expansion of the generalised metric, which reproduces the Non-Riemannian formulation of DFT at the (finite) leading order, and the c-expansion of the generalised frame, which contains divergences. We also extend this approach to the non-Abelian gauge field of Heterotic DFT assuming a convergent expansion for the O(D, D + n) generalised metric. From this proposal, we derive a novel c-expansion for the bosonic part of the heterotic supergravity which is, by construction, compatible with O(D, D)-symmetry.

Probing the quantum nature of gravity using a Bose-Einstein condensate

The effect of noise induced by gravitons has been investigated using a Bose-Einstein condensate. The general complex scalar field theory with a quadratic self-interaction term has been considered in the presence of a gravitational wave. The gravitational wave perturbation is then considered as a sum of discrete Fourier modes in the momentum space. Varying the action and making use of the principle of least action, one obtains two equations of motion corresponding to the gravitational perturbation and the time-dependent part of the pseudo-Goldstone boson. Coming to an operatorial representation and quantizing the phase space variables via appropriately introduced canonical commutation relations between the canonically conjugate variables corresponding to the graviton and bosonic part of the total system, one obtains a proper quantum gravity setup. Then we obtain the Bogoliubov coefficients from the solution of the time-dependent part of the pseudo-Goldstone boson and construct the covariance metric for the bosons initially being in a squeezed state. The entries of the covariance matrix now involves a stochastic contribution which results in an operatorial stochastic structure of the quantum Fisher information. Using the stochastic average of the Fisher information, we obtain a lower bound on the amplitude parameter of the gravitational wave. As the entire calculation is done at zero temperature, the bosonic system, by construction, will behave as a Bose-Einstein condensate. For a Bose-Einstein condensate with a single mode, we observe that the lower bound of the expectation value of the square of the uncertainty in the amplitude measurement does not become infinite when the total observational term approaches zero. It always has a finite value if the gravitons are initially in a squeezed state with high enough squeezing. In order to sum over all possible momentum modes, we next consider a noise term with a suitable Gaussian weight factor which decays over time. We then obtain the lower bound on the final expectation value of the square of the variance in the amplitude parameter. Because of the noise induced by the graviton, there is a minimum value of the measurement time below which it is impossible to detect any gravitational wave using a Bose-Einstein condensate. Finally, we consider interaction between the phonon modes of the Bose-Einstein condensate which results in a decoherence. We observe that the decoherence effect becomes significant for gravitons with minimal squeezing. Published by the American Physical Society 2024

Heterotic integrable deformation of the principal chiral model

A novel classically integrable model is proposed. It is a deformation of the two-dimensional principal chiral model, embedded into a heterotic σ model by a particular heterotic gauge field. This is inspired by the bosonic part of the heterotic σ model and its recent Hamiltonian formulation in terms of O(d,d+n)-generalized geometry in Hatsuda [Gauged double field theory, current algebras and heterotic sigma models, ]. Classical integrability is shown by the construction of a Lax pair and a classical R matrix. The latter is almost of the canonical form with a twist function and solves the classical Yang-Baxter equation. Published by the American Physical Society 2024

Extending third quantization with commuting observables: a dissipative spin-boson model

We consider the spectral and initial value problem for the Lindblad–Gorini–Kossakowski–Sudarshan master equation describing an open quantum system of bosons and spins, where the bosonic parts of the Hamiltonian and Lindblad jump operators are quadratic and linear respectively, while the spins couple to bosons via mutually commuting spin operators. Needless to say, the spin degrees of freedom can be replaced by any set of finite-level quantum systems. A simple, yet non-trivial example of a single open spin-boson model is worked out in some detail.

Complex powers of the wave operator and the spectral action on Lorentzian scattering spaces

We consider perturbations of Minkowski space as well as more general spacetimes on which the wave operator \square_{g} is known to be essentially self-adjoint. We define complex powers (\square_{g}-i\varepsilon)^{-\alpha} by functional calculus, and show that the trace density exists as a meromorphic function of \alpha . We relate its poles to geometric quantities, in particular to the scalar curvature. The results allow us to formulate a spectral action principle which serves as a simple Lorentzian model for the bosonic part of the Chamseddine–Connes action. Our proof combines microlocal resolvent estimates, including radial propagation estimates, with uniform estimates for the Hadamard parametrix. The arguments work in Lorentzian signature directly and do not rely on transition from the Euclidean setting.

Non-Lorentzian IIB supergravity from a polynomial realization of SL(2, ℝ)

We derive the action and symmetries of the bosonic sector of non-Lorentzian IIB supergravity by taking the non-relativistic string limit. We find that the bosonic field content is extended by a Lagrange multiplier that implements a restriction on the Ramond-Ramond fluxes. We show that the SL(2, ℝ) transformation rules of non-Lorentzian IIB supergravity form a novel, nonlinear polynomial realization. Using classical invariant theory of polynomial equations and binary forms, we will develop a general formalism describing the polynomial realization of SL(2, ℝ) and apply it to the special case of non-Lorentzian IIB supergravity. Using the same formalism, we classify all the relevant SL(2, ℝ) invariants. Invoking other bosonic symmetries, such as the local boost and dilatation symmetry, we show how the bosonic part of the non-Lorentzian IIB supergravity action is formed uniquely from these SL(2, ℝ) invariants. This work also points towards the concept of a non-Lorentzian bootstrap, where bosonic symmetries in non-Lorentzian supergravity are used to bootstrap the bosonic dynamics in Lorentzian supergravity, without considering the fermions.

Scalar, fermionic and supersymmetric field theories with subsystem symmetries in d + 1 dimensions

We study various non-relativistic field theories with exotic symmetries called subsystem symmetries, which have recently attracted much attention in the context of fractons. We start with a scalar theory called ϕ-theory in d + 1 dimensions and discuss its properties studied in literature for d ≤ 3 such as self-duality, vacuum structure, ’t Hooft anomaly, anomaly inflow and lattice regularization. Next we study a theory called chiral ϕ-theory which is an analogue of a chiral boson with subsystem symmetries. Then we discuss theories including fermions with subsystem symmetries. We first construct a supersymmetric version of the ϕ-theory and dropping its bosonic part leads us to a purely fermionic theory with subsystem symmetries called ψ-theory. We argue that lattice regularization of the ψ-theory generically suffers from an analogue of doubling problem as previously pointed out in the d = 3 case. We propose an analogue of Wilson fermion to avoid the “doubling” problem. We also supersymmetrize the chiral ϕ-theory and dropping the bosonic part again gives us a purely fermionic theory. We finally discuss vacuum structures of the theories with fermions and find that they are infinitely degenerate because of spontaneous breaking of subsystem symmetries.

Software tools for computing EW chiral amplitudes

We present an implementation of the Electroweak Chiral Lagrangian (also denoted as Higgs Effective Theory) in several high energy physics Mathematica packages. In particular, we implement the bosonic part of the electoweak Lagrangian up to next-to-leading order for FeynRules, FeynArts and FeynCalc. These tools are publicly available and can be used to readily calculate the Feynman rules and amplitudes in the theory.

Noncommutativity and nonassociativity of type II superstring with coordinate dependent RR field — the general case

In this paper we consider non-commutativity that arises from T-duality of bosonic coordinates of type II superstring in presence of coordinate dependent Ramond-Ramond field. Action with such choice of the background fields is not translational invariant. Consequently, we will employ generalization of Buscher procedure that can be applied to cases that have coordinate dependent fields and that do not possess translational isometry. Bosonic part of newly obtained T-dual theory is non-local and defined in non-geometric double space spanned by Lagrange multipliers yμ and double coordinate ∆Vμ. We will apply Buscher procedure once more on T-dual theory to check if original theory can be salvaged. Finally, we will use T-dual transformation laws along with Poisson brackets of original theory to derive Poisson bracket structure of T-dual theory.

Nonlinear [formula omitted] supersymmetry and 3D supersymmetric Born-Infeld theory

Dp-branes acquire effective nonlinear descriptions whose bosonic part is related to the Born-Infeld action. This nonlinearity has been proven to be a consequence of the partial N=2→N=1 supersymmetry breaking, originating from the solitonic nature of the branes. In this work, we focus on the effective descriptions of D2-branes. Using the Goldstone multiplet interpretation of the action and the method of nilpotent N=2 superfields, we construct the 3D, N=1 superspace effective action which makes the first supersymmetry manifest and realizes the second, spontaneously broken, supersymmetry nonlinearly. We show that there are two such supersymmetric extensions of the 3D Born-Infeld action which correspond to the dynamics of the 3D Maxwell-Goldstone multiplet and the 3D projection of the Tensor-Goldstone multiplet respectively. Moreover, we demonstrate that these results are derived by applying the constrained superfield approach on the N=2,D=3 vector and chiral multiplets after expanding them around a nontrivial vacuum. We find that these two descriptions are related by a duality transformation which results in the inversion of a dimensionless parameter. For both descriptions we derive the explicit bosonic and fermionic parts of the 3D super Born-Infeld action. Finally, consider the deformation of the Maxwell-Goldstone superspace action by the characteristic Chern-Simons-like, gauge invariant, mass term.

Non-perturbative phase structure of the bosonic BMN matrix model

We study the bosonic part of the BMN matrix model for wide ranges of temperatures, values of the deformation parameter, and numbers of colors 16 ≤ N ≤ 48. Using lattice computations, we analyze phase transitions in the model, observing a single first-order transition from a uniform to a gapped phase for all values of the deformation parameter. We study the functional form of the dependence of the critical temperature on the deformation parameter, to describe how our results smoothly interpolate between the limits of the bosonic BFSS model and the gauged Gaussian model.

S-wave pion-pion scattering lengths from nucleon-meson fluctuations

We present calculations of the $S$-wave isospin-zero and isospin-two pion-pion scattering lengths within a nucleon-meson model with parity doubling. Both scattering lengths are computed in various approximations, ranging from a mean-field (MF) calculation toward the inclusion of loop corrections by means of the functional renormalization group (FRG). The bosonic part of the investigated nucleon-meson model is formulated in terms of stereographic projections as a ``natural'' set of coordinates on the respective vacuum manifold. We thereby elucidate subtleties concerning the truncation of the effective action with respect to higher-derivative pion interactions and the ``successful'' computation of the scattering lengths. As the main result, we find simultaneous agreement for the isospin-zero and isospin-two scattering lengths with experimental data within the ${\mathrm{LPA}}^{\ensuremath{'}}$ truncation of the FRG, together with chiral-symmetry breaking (roughly) occurring at the characteristic scale of $4\ensuremath{\pi}{f}_{\ensuremath{\pi}}$. The isoscalar $\ensuremath{\sigma}$ mass is dynamically generated by the FRG integration of momentum modes and is a prediction of the model. It ends being of the order of 500 MeV, i.e., much lower than the value ($>1\text{ }\text{ }\mathrm{GeV}$) found in MF or one-loop treatment of this or related models. Finally, the convergence of the corresponding low-energy expansion of the quantum effective action in terms of pion momenta is discussed.

Noncommutativity and Nonassociativity of Type II Superstring with Coordinate Dependent RR Field

AbstractIn this paper we will consider noncommutativity that arises from bosonic T‐dualization of type II superstring in presence of Ramond‐Ramond (RR) field, which linearly depends on the bosonic coordinates . The derivative of the RR field is infinitesimal. We will employ generalized Buscher procedure that can be applied to cases that have coordinate dependent background fields. Bosonic part of newly obtained T‐dual theory is non‐local. It is defined in non‐geometric space spanned by Lagrange multipliers . We will apply generalized Buscher procedure once more on T‐dual theory and prove that original theory can be salvaged. Finally, we will use T‐dual transformation laws along with Poisson brackets of original theory to derive Poisson bracket structure of T‐dual theory and nonassociativity relation. Noncommutativity parameter depends on the supercoordinates , and , while nonassociativity parameter is a constant tensor containing infinitesimal .

The E10 Wheeler-DeWitt operator at low levels

We consider the Wheeler-DeWitt operator associated with the bosonic part of the Hamiltonian of D = 11 supergravity in a formulation with only the spatial components of the three-form and six-form fields, and compare it with the E10 Casimir operator at low levels, to show that these two operators precisely match modulo spatial gradients up to and including mathfrak{gl} 10 level ℓ = 2. The uniqueness of the E10 Casimir operator eliminates all ordering ambiguities in the quantum Hamiltonian, at least up to the level considered. Beyond ℓ ≥ 3 the two operators are expected to start to differ from each other, as they do so for the classical expressions. We then consider truncations of the E10 Wheeler-DeWitt operator for various finite-dimensional subgroups of E10 in order to exhibit the automorphic properties of the associated wave functions and to show that physically sensible wave functions generically vanish at the cosmological singularity, thus providing new and more sophisticated examples of DeWitt’s proposed mechanism for singularity resolution in quantum gravity. Our construction provides novel perspectives on several unresolved conceptual issues with the Wheeler-DeWitt equation, such as the question of observables in quantum gravity, or the issue of emergent space and time in a purely algebraic framework. We also highlight remaining open questions of the E10 framework.

4D effective action from the non-Abelian DBI action with a magnetic flux background

We study a systematic derivation of four dimensional $\mathcal{N}=1$ supersymmetric effective theory from ten dimensional non-Abelian Dirac-Born-Infeld action compactified on a six dimensional torus with magnetic fluxes on the D-branes. We find a new type of matter K\"{a}hler metric while gauge kinetic function and superpotential are consistent with previous studies. For the ten dimensional action, we use a symmetrized trace prescription and focus on the bosonic part up to $\mathcal{O}(F^4)$. In the presence of the supersymmetry, four dimensional chiral fermions can be obtained via index theorem. The new matter K\"{a}hler metric is independent of flavor but depends on the fluxes, 4D dilaton, K\"{a}hler moduli and complex structure moduli, and will be always positive definite if an induced Ramond-Ramond charge of the D-branes on which matters are living are positive. We read the superpotential from an F-term scalar quartic interaction derived from the ten dimensional action and the contribution of the new matter K\"{a}hler metric to the scalar potential which we derive turns out to be consistent with the supergravity formulation.

Two approaches to quantum gravity and M-(atrix) theory at large number of dimensions

A Gaussian approximation to the bosonic part of M-(atrix) theory with mass deformation is considered at large values of the dimension [Formula: see text]. From the perspective of the gauge/gravity duality this action reproduces with great accuracy the stringy Hagedorn phase transition from a confinement (black string) phase to a deconfinement (black hole) phase whereas from the perspective of the matrix/geometry approach this action only captures a remnant of the geometric Yang–Mills-to-fuzzy-sphere phase where the fuzzy sphere solution is only manifested as a three-cut configuration termed the “baby fuzzy sphere” configuration. The Yang–Mills phase retains most of its characteristics with two exceptions: (i) the uniform distribution inside a solid ball suffers a crossover at very small values of the gauge coupling constant to a Wigner’s semicircle law, and (ii) the uniform distribution at small values of the temperatures is nonexistent.

Novel 3D supersymmetric massive Yang-Mills theory

We construct three-dimensional, $\mathcal{N}=1$ off-shell supersymmetric massive Yang-Mills (YM) theory whose YM equation is ``third-way'' consistent. This means that the field equations of this model do not come from variation of a local action without additional fields, yet the gauge-covariant divergence of the YM equation still vanishes on shell. To achieve this, we modify the massive Majorana spinor equation so that its supersymmetry variation gives a modified YM equation whose bosonic part coincides with the third-way consistent pure massive YM model.

Existence of a supersymmetric massless ground state of the SU(N) matrix model globally on its valleys

In this work we consider the existence and uniqueness of the ground state of the regularized Hamiltonian of the Supermembrane in dimensions D = 4, 5, 7 and 11, or equivalently the SU(N) Matrix Model. That is, the 0+1 reduction of the 10-dimensional SU(N) Super Yang-Mills Hamiltonian. This ground state problem is associated with the solutions of the inner and outer Dirichlet problems for this operator, and their subsequent smooth patching (glueing) into a single state. We have discussed properties of the inner problem in a previous work, therefore we now investigate the outer Dirichlet problem for the Hamiltonian operator. We establish existence and uniqueness on unbounded valleys defined in terms of the bosonic potential. These are precisely those regions where the bosonic part of the potential is less than a given value V0, which we set to be arbitrary. The problem is well posed, since these valleys are preserved by the action of the SU(N) constraint. We first show that their Lebesgue measure is finite, subject to restrictions on D in terms of N. We then use this analysis to determine a bound on the fermionic potential which yields the coercive property of the energy form. It is from this, that we derive the existence and uniqueness of the solution. As a by-product of our argumentation, we show that the Hamiltonian, restricted to the valleys, has spectrum purely discrete with finite multiplicity. Remarkably, this is in contrast to the case of the unrestricted space, where it is well known that the spectrum comprises a continuous segment. We discuss the relation of our work with the general ground state problem and the question of confinement in models with strong interactions.

Fermion-enhanced first-order phase transition and chiral Gross-Neveu tricritical point

The fluctuations of massless Dirac fermion can not only turn a first-order bosonic phase transition (in the Landau sense) to a quantum critical point, but also work reversely to enhance the first-order transition itself, depending on the implementation of finite size effects in the coupling corrections. Here, we report a case study of the latter by employing quantum Monte Carlo simulation upon a lattice model in which the bosonic part featuring the Landau-Devonshire first-order phase transition and Yukawa coupled to the Dirac fermions. We find that the parameter range for the first-order phase transition becomes larger as the Yukawa coupling increases and the microscopic mechanism of this phenomena is revealed, at a quantitative level, as the interplay between the critical fluctuations and the finite-size effects. Moreover, the scaling behavior at the separation point between the first-order and the continuous phase transitions is found to belong to the chiral tricritical Gross-Neveu universality. Our result demonstrates that the interplay of massless Dirac fermions, critical fluctuations and the finite size effects could trigger a plethora of interesting phenomena and therefore great care is called for when making generalizations.

World-volume effective theories of locally non-geometric branes

We study world-volume effective theories of five-branes in type II string theories. We determine the bosonic zero-modes of the NS5-brane, the Kaluza-Klein monopole, the exotic Q5-, R5-branes and a space-filling brane, by direct calculations within the formalism of double field theory (DFT). We show that these zero-modes are Nambu-Goldstone modes associated with the spontaneously broken gauge symmetries in DFT. They are organized into the bosonic part of the six-dimensional mathcal{N} = (1) vector and the mathcal{N} = (2, 0) tensor multiplets. Among other things, we examine the locally non-geometric R5-branes and space-filling branes that are characterized by the winding space. We also study effective theories of five-branes with string worldsheet instanton corrections.