This paper is about the use of a novel, exact functional quantization method as applied to two commonly studied actions in theoretical physics. The functional method in question has its roots in the exact renormalisation group flow techniques pioneered by Wilson, but with the flow parameter not limited to the familiar momentum cutoff. Finding a configuration satisfying an expression for the exact effective action which does not vary with this parameter provides the basis for finding solutions to the physical actions we study. Firstly, the method is applied to an expression for the bare action of the pseudo-scalar axion used to explain the strong CP problem in QCD. When quantized, we find that the effective potential of the axion, when interactions are not considered, is necessarily flattened by spinodal instability effects. We regard this flattening asrepresenting the very early stage in the development of the axion potential, when the Peccei-Quinn U(1) symmetry is spontaneously broken resulting in a double-well potential. Using commonly quoted values for the parameters of such a potential, we devise an expression for the energy density of the emerging axion potential and this is compared to dark energy. We then apply the functional method to the bosonic string with time varying graviton, dilaton and antisymmetric tensor (resulting in the string-axion) background fields. We achieve a demonstration of conformal invariance in a non-perturbative manner in the beta functions, contrasting with conventional string cosmology where cancellation of a perturbative expansion is performed. We then offer some hints as to possible cosmological implications of our configuration in terms of optical anisotropy.
We study sets of oscillators that have high quantum occupancy and that interact by exchanging quanta. It is shown by analytical arguments and numerical simulation that such systems obey classical equations of motion only on time scales of order their relaxation time $τ$ and not longer than that. The results are relevant to the cosmology of axions and axion-like particles.
We study the renormalization flow of axion electrodynamics, concentrating on the non-perturbative running of the axion-photon coupling and the mass of the axion (like) particle. Due to a non-renormalization property of the axion-photon vertex, the renormalization flow is controlled by photon and axion anomalous dimensions. As a consequence, momentum-independent axion self-interactions are not induced by photon fluctuations. The non-perturbative flow towards the ultraviolet exhibits a Landau-pole-type behavior, implying that the system has a scale of maximum UV extension and that the renormaliz…
Conformal invariance for bosonic strings in time-dependent backgrounds of graviton, dilaton and Kalb-Ramond field is obtained by imposing Weyl-beta functions to be homogeneous in time, to all orders in $α^{'}$. This construction is possible in any target space dimension, as a result of the non-trivial background configurations. The electromagnetic effects of the antisymmetric tensor field, when coupled to an Abelian (electromagnetic) gauge field, are discussed in the framework of a four-dimensional Minkowski Universe, for concreteness. Non-trivial optical activity is demonstrated, which consti…
Axions play a central role in many realizations of large field models of inflation and in recent alternative mechanisms for generating primordial tensor modes in small field models. If these axions couple to gauge fields, the coupling produces a tachyonic instability that leads to an exponential enhancement of the gauge fields, which in turn can decay into observable scalar or tensor curvature perturbations. Thus, a fully self-consistent treatment of axions during inflation is important, and in this work we discuss the perturbative constraints on axions coupled to gauge fields. We show how the…
Axion like particles (ALPs) are quite generic in many scenarios for physics beyond the Standard Model, they are pseudoscalar Nambu-Goldstone bosons, and appear once any global $U(1)$ symmetry is broken spontaneously. The ALPs can gain mass from various non-perturbative quantum effects, such as anomalies or instantons. ALPs can couple to the matter sector incluidng a scalar condensate such as inflaton or moduli field via derivative interactions, which are suppressed by the axion {\it decay constant}, $f_χ$ . Although weakly interacting, the ALPs can be produced abundantly from the coherent osci…
We discuss the role of Minkowski 3-forms in flux string vacua. In these vacua all internal closed string fluxes are in one to one correspondence with quantized Minkowski 4-forms. By performing a dimensional reduction of the $D=10$ Type II supergravity actions we find that the 4-forms act as auxiliary fields of the Kahler and complex structure moduli in the effective action. We show that all the RR and NS axion dependence of the flux scalar potential appears through the said 4-forms. Gauge invariance of these forms then severely restricts the structure of the axion scalar potentials. Combined w…
The modular invariance of the one-loop partition function of the closed bosonic string in four dimensions in the presence of certain homogeneous exact pp-wave backgrounds is studied. In the absence of an axion field the partition function is found to be modular invariant. In the presence of an axion field modular invariace is broken. This can be attributed to the light-cone gauge which breaks the symmetry in the $σ$-, $t$-directions. Recovery of this broken modular invariance suggests the introduction of twists in the world-sheet directions. However, one needs to go beyond the light-cone gauge…
Bosonic end perturbative calculations for quantum mechanical anyon systems require a regularization. I regularize by adding a specific $δ$-function potential to the Hamiltonian. The reliability of this regularization procedure is verified by comparing its results for the 2-anyon in harmonic potential system with the known exact solutions. I then use the $δ$-function regularized bosonic end perturbation theory to test some recent conjectures concerning the unknown portion of the many-anyon spectra.
We study a class of gauge groups that can automatically yield a perturbatively exact Peccei-Quinn symmetry, and we outline a model in which the axion quality problem is solved at all operator dimensions. Gauge groups belonging to this class can also enforce and protect accidental symmetries of the clockwork type, and we present a toy model where an `invisible' axion arises from a single breaking of the gauge and global symmetries.
We review a construction called Non-Perturbative Gauge-Higgs Unification which is a rather rare type of Higgs mechanism that is a pure quantum and bosonic effect. It is constructed on a five-dimensional "orbifold lattice" with SU(2) bulk gauge symmetry and a (spontaneously broken) Abelian-Higgs like theory on the boundaries.
We present an explicit embedding of axionic N-flation in type IIB string compactifications where most of the Kahler moduli are stabilised by perturbative effects, and so are hierarchically heavier than the corresponding N >> 1 axions whose collective dynamics drives inflation. This is achieved in the framework of the LARGE Volume Scenario for moduli stabilisation. Our set-up can be used to realise a model of either inflation or quintessence, just by varying the volume of the internal space which controls the scale of the axionic potential. Both cases predict a very high scale of supersymmetry …
We present a study of the mechanism of anomaly cancellation using only transverse invariant amplitudes on anomaly diagrams at higher perturbative orders. The method is the realization of the Green-Schwarz (GS) mechanism at field theory level, which restores the Ward identities by a subtraction of the anomaly pole. Some of the properties of the GS vertex are analyzed both in the context of unitarity and of the organization of the related perturbative expansion. We investigate the role played by the GS and the Wess-Zumino vertices in the anomalous magnetic moment of the muon and in the hyperfine…
We review some exact solitonic solutions of string theory with higher-membrane structure. These include an axionic instanton solution of bosonic string theory as well as multi-instanton and multimonopole solutions of heterotic string theory. The heterotic solutions reveal some interesting aspects of string theory as a theory of quantum gravity.
Continuing with the ideas of (section 4 of) [1], after inclusion of perturbative and non-perturbative alpha' corrections to the Kaehler potential and (D1- and D3-) instanton generated superpotential, we show the possibility of slow-roll axionic inflation in the large volume limit of Swiss-Cheese Calabi-Yau orientifold compactifications of type IIB string theory. We also include one- and two-loop corrections to the Kaehler potential but find the same to be subdominant to the (perturbative and non-perturbative) alpha' corrections. The NS-NS axions provide a flat direction for slow-roll inflation…
We study the interplay between extrema of axion potentials, Kahler moduli stabilization and the swampland criteria. We argue that moving away from the minima of non-perturbatively generated axion potentials can lead to a runaway behavior of moduli that govern the couplings in the effective field theory. The proper inclusion of these degrees of freedom resolves the conflict between periodic axion potentials and the gradient de Sitter criterion, without the need to invoke the refined de Sitter criterion. We investigate the possibility of including this runaway direction as a model of quintessenc…
Tachyon condensation on a bosonic D-brane was recently demonstrated numerically in Witten's open string field theory with level truncation approximation. This non-perturbative vacuum, which is obtained by solving the equation of motion, has to satisfy furthermore the requirement of BRST invariance. This is indispensable in order for the theory around the non-perturbative vacuum to be consistent. We carry out the numerical analysis of the BRST invariance of the solution and find that it holds to a good accuracy. We also mention the zero-norm property of the solution. The observations in this pa…
We put forward the Axionic String Ansatz (ASA), which provides a unified description for the worldsheet dynamics of confining strings in pure Yang--Mills theory both in $D=3$ and $D=4$ space-time dimensions. The ASA is motivated by the excitation spectrum of long confining strings, as measured on a lattice, and by recently constructed integrable axionic non-critical string models. According to the ASA, pure gluodynamics in 3D is described by a non-critical bosonic string theory without any extra local worldsheet degrees of freedom. We argue that this assumption fixes the set of quantum numbers…
We discuss the contribution of axion-like excitations (ALE) to the vacuum birrefringence in the limit $m_A \gtrsim ω$, where $m_A$ is the mass of the excitation and $ω$ the energy of test photons interacting with an external (intense) magnetic field. The relevance of this term with respect to the QED contribution depends on the ratio $g_A/m_A$ and, from present bounds on the mass and the coupling constant $g_A$, we find that in the present low energy regime, it ranges from $10^{-14}$ to $10^2$ suggesting an interesting alternative to explore.
In bosonic end perturbative calculations for quantum mechanical anyon systems a regularization and renormalization procedure, analogous to those used in field theory, is necessary. I examine the reliability and the physical interpretation of the most commonly used bosonic end regularization procedures. I then use the regularization procedure with the most transparent physical interpretation to derive some bosonic end perturbation theory results on anyon spectra, including a 3-anyon ground state energy.
The fundamental fermion representations of causal spinor fields have previously been demonstrated to describe free Dirac fermions, as well as incorporate \emph{only} the observed degrees of freedom for local gauge invariance. In this paper, the first non-trivial boson representations of causal spinors will be presented. The general unitary mixing of degenerate bosonic spinors will be developed, and then applied to electro-weak bosons satisfying appropriate kinematic constraints. The resulting mass ratios are seen to be consistent with reported measured values for these bosons.
We study the world-volume theory of a bosonic membrane perturbatively and discuss if one can obtain any conditions on the number of space-time dimensions from the consistency of the theory. We construct an action which is suitable for such a study. In order to study the theory perturbatively we should specify a classical background around which perturbative expansion is defined. We will discuss the conditions which such a background should satisfy to deduce the critical dimension. Unfortunately we do not know any background satisfying such conditions. In order to get indirect evidences for the…
We investigate viable scenarios with various axions in the context of supersymmetric field theory and in globally consistent D-brane models. The Peccei-Quinn symmetry is associated with an anomalous U(1) symmetry, which acquires mass at the string scale but remains as a perturbative global symmetry at low energies. The origin of the scalar Higgs-axion potential from F-, D- and soft breaking terms is derived, and two Standard Model examples of global intersecting D6-brane models in Type II orientifolds are presented, which differ in the realisation of the Higgs sector and in the hidden sector, …
The duality properties of perturbative string characters associated with the transverse space-time rotations are studied. T duality is achieved by suitably integrating over the total momentum, contrary to earlier discussions. The O(8) triality properties of the characters for critical superstrings, are derived. This shows the existence of a third formulation (unnoticed so far to our knowledge) equivalent to, but different from the ones of Neveu-Schwarz-Ramond, and Green-Schwarz. Projectors in the NS and R sectors are defined in the GS formalism. The consequences of supersymmetry are neatly der…
The weakly-coupled heterotic string is known to have problems of dilaton/moduli stabilization, supersymmetry breaking (by hidden-sector gaugino condensation), gauge coupling unification (or the Newton's constant), QCD axion, as well as cosmological problems. We study these problems by adopting the viewpoint that they arise mostly due to our limited calculational power, little knowledge of the vacuum structure, and an inappropriate treatment of gaugino condensation. It turns out that these problems can be solved or are much less severe after a more consistent and complete treatment. There are t…
We study the bosonic part of the BMN matrix model for wide ranges of temperatures, values of the deformation parameter, and numbers of colors $16 \leq N \leq 48$. 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.
Consistent frameworks of quantum gravity often predict the existence of large numbers of ultralight pseudoscalar degrees of freedom, forming the phenomenological landscape of the String Axiverse. The complexity of the extra-dimensional compactification manifolds and vacua determine that these fields could possess parameters with cosmologically significant scales, which span many decades. Astrophysical observations of stellar binary and supermassive black hole systems can be used to exclude the existence of certain ultralight massive bosons, via the superradiance phenomenon. In this work it is …
We perform a detailed analytical and numerical analysis of the multi-field evolution of Fibre Inflation and show that, regardless of the microscopic realisation of the model, the mass-squared of one of the two ultra-light axions becomes always negative during inflation. This implies that the corresponding isocurvature perturbations experience a potential geometrical destabilisation which seems to bring the system away from the perturbative regime. Therefore we conclude that a full understanding of the inflationary evolution of Fibre Inflation can be achieved only via a non-perturbative analysi…
We investigate the axion inflation model derived by poly-instanton effects in type II superstring theories. Poly-instanton effects are instanton effects corrected by another instanton and it can generate the modulus-axion potential with the double exponential function. Although the axion has a period of small value, this potential can have a flat region because its derivatives are exponentially suppressed by non-perturbative effects. From the view point of the cosmic inflation, such potential is interesting. In this paper, we numerically study the possibilities for realizing the cosmic inflati…
In recent times, a considerable effort has been dedicated to identify certain conditions -- the so-called swampland conjectures -- with an eye on identifying effective theories which have no consistent UV-completions in string theory. In this paper, we examine the anti-de Sitter vacua corresponding to solutions which arise from purely non-perturbative contributions to the superpotential and show that these solutions satisfy the (axionic) weak gravity conjecture and the AdS-moduli scale separation conjecture. We also sketch out their advantages over other constructions.
In this paper, colorless bilocal fields are employed to study the large $N$ limit of both fermionic and bosonic vector models. The Jacobian associated with the change of variables from the original fields to the bilocals is computed exactly, thereby providing an exact effective action. This effective action is shown to reproduce the familiar perturbative expansion for the two and four point functions. In particular, in the case of fermionic vector models, the effective action correctly accounts for the Fermi statistics. The theory is also studied non-perturbatively. The stationary points of th…
The study of axion models and quantum corrections to their potential has experienced great progress by phrasing the axion potential in terms of a 3-form field eating up the 2-form field dual to the axion. Such reformulation of the axion potential has been described for axion monodromy models, and for axion potentials from non-perturbative gauge dynamics. In this paper we propose a 3-form description of the axion potentials from non-gauge D-brane instantons. Interestingly, the required 3-form field does not arise in the underlying geometry, but rather shows up in the KK compactification in the …
New and surprisingly simple representation is found for the heterotic string bosonic effective action in three dimensions in terms of complex potentials. The system is presented as a Kähler $σ$--model using complex symmetric $2\times 2$ matrix (matrix dilaton--axion) which depends linearly on three Ernst--type potentials and transforms under $U$--duality via matrix valued $SL(2,R)$. Two discrete automorphisms relating ten isometries of the target space (U--duality transformations) are found and used to generate the non--trivial Ehlers--Harrison sector by a map from the trivial gauge sector. Fi…
An attractive candidate for the inflaton is an axion slowly rolling down a flat potential protected by a perturbative shift symmetry. Realisations of this idea within large field, natural and monomial inflation have been disfavoured by observations and are difficult to embed in string theory. We show that subleading, but significant non-perturbative corrections can superimpose sharp cliffs and gentle plateaus into the potential, whose overall effect is to enhance the number of e-folds of inflation. Sufficient e-folds are therefore achieved for smaller field ranges compared to the potential wit…
The QCD axion acquires the potential through the non-perturbative effect of the QCD matters around the QCD phase transition. During this period, the direct interaction between the axion and the QCD matters sets in. Focusing on the impact of this direct interaction, we propose two scenarios where the fluctuation of the axion can rapidly grow, potentially leading to the formation of axion miniclusters even if the Peccei-Quinn (PQ) symmetry was already broken during inflation. The first scenario assumes that the primordial curvature perturbation at the horizon scale during the QCD epoch was signi…
Quantization of the bosonic string around the classical, perturbative vacuum is not consistent for spacetime dimensions 2<d<26. Recently we have showed that at large d there is another so-called mean field vacuum. Here we extend this mean field calculation to finite d and show that the corresponding mean field vacuum is stable under quadratic fluctuations for 2<d<26. We point out the analogy with the two-dimensional O(N)-symmetric sigma-model, where the 1/N-vacuum is very close to the real vacuum state even for finite N, in contrast to the perturbative vacuum.
In this paper we work in perturbative quantum gravity and we introduce a new effective model for gravity. Expanding the Einstein-Hilbert Lagrangian in graviton field powers we have an infinite number of terms. In this paper we study the possibility of an interpretation of more than three graviton interacting vertices as effective vertices of a most fundamental theory that contain tensor fields. Here we introduce a Lagrangian model named I.T.B (Intermediate Tensor Boson) where four gravitational "pseudo-currents" that contain two gravitons couple to three massive tensorial fields of rank 1, 3, …
We investigate the possibility of enhancement of effective axion decay constant in well controlled constructions in string theory. To this end, we study the dynamics of axions arising in the compactifications of type IIA string theory on Calabi-Yau orientifolds with background fluxes (with non-perturbative effects included to ensure stabilization of all moduli). In this setup, we attempt to obtain large effective axion decay constant in two different ways: by searching for a direction in field space in which the potential is sufficiently flat and by arriving at a very explicit stringy embeddin…
Axions are among the best motivated dark matter candidates. Their production in the early Universe by the vacuum misalignment mechanism gives rise to isocurvature perturbations, which are constrained by cosmic microwave background measurements. In this paper, we compute the axion isocurvature power spectrum using spectral expansion in the stochastic Starobinsky-Yokoyama formalism, which captures non-linear effects in the axion dynamics. In contrast to most of the existing literature, we focus on high inflationary Hubble rates of order $10^{13}~{\rm GeV}$, and demonstrate that there is a signif…
We show how D-instanton corrections modify the dilaton-axion profile emitted by an O7/D7 system turning it into the non-singular F-theory background which corresponds to the effective coupling on a D3 probe.
1. Introduction 2. Models: the QCD axion; the strong CP problem; PQWW, KSVZ, DFSZ; anomalies, instantons and the potential; couplings; axions in string theory 3. Production and I.C.'s: SSB and non-perturbative physics; the axion field during inflation and PQ SSB; cosmological populations - decay of parent, topological defects, thermal production, vacuum realignment 4. The Cosmological Field: action; background evolution; misalignment for QCD axion and ALPs; cosmological perturbation theory - i.c.'s, early time treatment, axion sound speed and Jeans scale, transfer functions and WDM; the Schrod…
We obtain axionic charged primordial black holes on a vacuum created gravitational pair of $(3{\bar 3})$-brane by the Kalb-Ramond field on a $D_4$-brane in presence of a background open string metric. The new geometries on an emergent pair of $(3{\bar 3})$-brane universe is shown to be influenced by the non-perturbative quantum effects underlying a geometric torsion in a second order formalism. The presence of small extra dimensions transverse to the pair in the formalism ensures dynamical scalar fields hidden to a $3$-brane or an anti 3-brane universe. We investigate the non-perturbative quan…
We extend the Vecchia-Veneziano-Witten (VVW) model of QCD in the chiral limit and for large colour number $N_c$, by introducing an effective dilaton-gluon coupling from which we derive both the axion and dilaton potentials. Furthermore, using a string inspired model, we determine a new interquark potential as a perturbative series in terms of the interquark distance $r$. Our potential goes beyond Dick one obtained in [8] and shares the same features as the Bian-Huang-Shen potential $V_{BHS}$ which depends only on odd powers of $r$ [22].
We study the axion monodromy inflation with a non-perturbatively generated sinusoidal term. The potential form is a mixture between the natural inflation and the axion monodromy inflation potentials. The sinusoidal term is subdominant in the potential, but leaves significant effects on the resultant fluctuation generated during inflation. A larger tensor-to-scalar ratio can be obtained in our model. We study two scenarios, single inflation scenario and the double inflation scenario. In the first scenario, the axion monodromy inflation with a sufficient number of e-fold generates a larger tenso…
We propose a new table-top experimental configuration for the direct detection of dark matter axions with mass in the $(10^{-6} \rm eV - 10^{-2} \rm eV)$ range using non-perturbative effects in a system with non-trivial spatial topology. Different from most experimental setups found in literature on direct dark matter axion detection, which relies on $\dotθ$ or $\vec{\nabla}θ$, we found that our system is in principle sensitive to a static $θ\geq 10^{-14}$ and can also be used to set limit on the fundamental constant $θ_{\rm QED}$ which becomes the fundamental observable parameter of the Maxwe…
We extend the perturbative double copy between radiating classical sources in gauge theory and gravity to the case of spinning particles. We construct, to linear order in spins, perturbative radiating solutions to the classical Yang-Mills equations sourced by a set of interacting color charges with chromomagnetic dipole spin couplings. Using a color-to-kinematics replacement rule proposed earlier by one of the authors, these solutions map onto radiation in a theory of interacting particles coupled to massless fields that include the graviton, a scalar (dilaton) $ϕ$ and the Kalb-Ramond axion fi…
Solutions of the classical $ϕ^4$-theory in Minkowski space-time are analyzed in a perturbation expansion in the nonlinearity. Using the language of Feynman diagrams, the solution of the Cauchy problem is expressed in terms of tree diagrams which involve the retarded Green's function and have one outgoing leg. In order to obtain general tree diagrams, we set up a "classical measurement process" in which a virtual observer of a scattering experiment modifies the field and detects suitable energy differences. By adding a classical stochastic background field, we even obtain all loop diagrams. The…
Renormalisation group flows connecting a $4-ε$ dimensional Hermitian field theory to a $\mathcal{PT}$-symmetric theory for a fermion coupled to an axion
