Symmetric scalars

We provide a complete classification of Poincar\'e-invariant scalar field theories with an enlarged set of classical symmetries to leading order in derivatives, namely for the so-called $P(X,\phi)$ theories, in two or more spacetime dimensions. We find only three possibilities: Dirac-Born-Infeld, Cuscuton and Scaling theories. The latter two classes of actions involve an arbitrary function of the scalar field. As an application, we use the scaling symmetry to derive an infinite set of constraints on the Wilsonian coefficients of the low-energy Effective Field Theory. Furthermore, we study the extension of these results to cosmological (FLRW) and (Anti-)de Sitter spacetimes. We find in particular that the Cuscuton action has a generic set of symmetries around any background spacetime that possesses Killing vector fields, while the DBI actions have well-known analogues that we summarize explicitly

Spatial curvature at the sound horizon

The effect of spatial curvature on primordial perturbations is controlled by  ΩK,0/cs2 , where  ΩK,0  is today's fractional density of spatial curvature and  cs  is the speed of sound during inflation. Here we study these effects in the limit  cs≪ 1 . First, we show that the standard cosmological soft theorems in flat universes are violated in curved universes and the soft limits of correlators can have non-universal contributions even in single-clock inflation. This is a consequence of the fact that, in the presence of spatial curvature, there is a gap between the spectrum of residual diffeomorphisms and that of physical modes. Second, there are curvature corrections to primordial correlators, which are not scale invariant. We provide explicit formulae for these corrections to the power spectrum and the bispectrum to linear order in curvature in single-clock inflation. We show that the large-scale CMB anisotropies could provide interesting new constraints on these curvature effects, and therefore on  ΩK,0/cs2 , but it is necessary to go beyond our linear-order treatment

Categorical Landau Paradigm for Gapped Phases

We propose a unified framework to classify gapped infra-red (IR) phases with categorical symmetries, leading to a generalized, categorical Landau paradigm. This is applicable in any dimension and gives a succinct, comprehensive, and computationally powerful approach to classifying gapped symmetric phases. The key tool is the symmetry topological field theory (SymTFT), which is a one dimension higher TFT with two boundaries, which we choose both to be topological. We illustrate the general idea for (1+1)d gapped phases with categorical symmetries and suggest higher-dimensional extensions.Comment: 4 pages + supplementary materia

Gapped Phases with Non-Invertible Symmetries: (1+1)d

We propose a general framework to characterize gapped infra-red (IR) phases of theories with non-invertible (or categorical) symmetries. In this paper we focus on (1+1)d gapped phases with fusion category symmetries. The approach that we propose uses the Symmetry Topological Field Theory (SymTFT) as a key input: associated to a field theory in d spacetime dimensions, the SymTFT lives in one dimension higher and admits a gapped boundary, which realizes the categorical symmetries. It also admits a second, physical, boundary, which is generically not gapped. Upon interval compactification of the SymTFT by colliding the gapped and physical boundaries, we regain the original theory. In this paper, we realize gapped symmetric phases by choosing the physical boundary to be a gapped boundary condition as well. This set-up provides computational power to determine the number of vacua, the symmetry breaking pattern, and the action of the symmetry on the vacua. The SymTFT also manifestly encodes the order parameters for these gapped phases, thus providing a generalized, categorical Landau paradigm for (1+1)d gapped phases. We find that for non-invertible symmetries the order parameters involve multiplets containing both untwisted and twisted sector local operators, and hence can be interpreted as mixtures of conventional and string order parameters. We also observe that spontaneous breaking of non-invertible symmetries can lead to vacua that are physically distinguishable: unlike the standard symmetries described by groups, non-invertible symmetries can have different actions on different vacua of an irreducible gapped phase. This leads to the presence of relative Euler terms between physically distinct vacua. We also provide a mathematical description of symmetric gapped phases as 2-functors from delooping of fusion category characterizing the symmetry to Euler completion of 2-vector spaces.Comment: 139 pages, v2: corrected an omission in the analysis of TY(Z_N) gapped phases reported by A. Antinucci, references adde

Nonsupersymmetric brane vacua in stabilized compactifications

We derive the equations for the nonsupersymmetric vacua of D3-branes in the presence of nonperturbative moduli stabilization in type IIB flux compactifications, and solve and analyze them in the case of two particular 7-brane embeddings at the bottom of the warped deformed conifold. In the limit of large volume and long throat, we obtain vacua by imposing a constraint on the 7-brane embedding. These vacua fill out continuous spaces of higher dimension than the corresponding supersymmetric vacua, and have negative effective cosmological constant. Perturbative stability of these vacua is possible but not generic. Finally, we argue that anti-D3-branes at the tip of the conifold share the same vacua as D3-branes.Comment: 17 pages, 1 figure, LaTeX. v2: references added, typo fixed. v3: version appearing in JHE

Chasing Brane Inflation in String-Theory

We investigate the embedding of brane anti-brane inflation into a concrete type IIB string theory compactification with all moduli fixed. Specifically, we are considering a D3-brane, whose position represents the inflaton $\phi$, in a warped conifold throat in the presence of supersymmetrically embedded D7-branes and an anti D3-brane localized at the tip of the warped conifold cone. After presenting the moduli stabilization analysis for a general D7-brane embedding, we concentrate on two explicit models, the Ouyang and the Kuperstein embeddings. We analyze whether the forces, induced by moduli stabilization and acting on the D3-brane, might cancel by fine-tuning such as to leave us with the original Coulomb attraction of the anti D3-brane as the driving force for inflation. For a large class of D7-brane embeddings we obtain a negative result. Cancelations are possible only for very small intervals of $\phi$ around an inflection point but not globally. For the most part of its motion the inflaton then feels a steep, non slow-roll potential. We study the inflationary dynamics induced by this potential.Comment: 34 pages, 4 figures. Final version published in JCA

Conformal consistency relations for single-field inflation

We generalize the single-field consistency relations to capture not only the leading term in the squeezed limit---going as 1/q^3, where q is the small wavevector---but also the subleading one, going as 1/q^2. This term, for an (n+1)-point function, is fixed in terms of the variation of the n-point function under a special conformal transformation; this parallels the fact that the 1/q^3 term is related with the scale dependence of the n-point function. For the squeezed limit of the 3-point function, this conformal consistency relation implies that there are no terms going as 1/q^2. We verify that the squeezed limit of the 4-point function is related to the conformal variation of the 3-point function both in the case of canonical slow-roll inflation and in models with reduced speed of sound. In the second case the conformal consistency conditions capture, at the level of observables, the relation among operators induced by the non-linear realization of Lorentz invariance in the Lagrangian. These results mean that, in any single-field model, primordial correlation functions of \zeta are endowed with an SO(4,1) symmetry, with dilations and special conformal transformations non-linearly realized by \zeta. We also verify the conformal consistency relations for any n-point function in models with a modulation of the inflaton potential, where the scale dependence is not negligible. Finally, we generalize (some of) the consistency relations involving tensors and soft internal momenta.Comment: 26 pages, 1 figure. v2. Corrected typos, notably a sign error in eq. (54). Matches JCAP published versio

DBI Inflation using a One-Parameter Family of Throat Geometries

We demonstrate the possibility of examining cosmological signatures in the DBI inflation setup using the BGMPZ solution, a one-parameter family of geometries for the warped throat which interpolate between the Maldacena-Nunez and Klebanov-Strassler solutions. The warp factor is determined numerically and subsequently used to calculate cosmological observables including the scalar and tensor spectral indices, for a sample point in the parameter space. As one moves away from the KS solution for the throat the warp factor is qualitatively different, which leads to a significant change for the observables, but also generically increases the non-Gaussianity of the models. We argue that the different models can potentially be differentiated by current and future experiments.Comment: 17 pages, 10 figures; v2: section 4 expanded, references added; v3: typos fixe

Universality in D-brane Inflation

We study the six-field dynamics of D3-brane inflation for a general scalar potential on the conifold, finding simple, universal behavior. We numerically evolve the equations of motion for an ensemble of more than 7 \times 10^7 realizations, drawing the coefficients in the scalar potential from statistical distributions whose detailed properties have demonstrably small effects on our results. When prolonged inflation occurs, it has a characteristic form: the D3-brane initially moves rapidly in the angular directions, spirals down to an inflection point in the potential, and settles into single-field inflation. The probability of N_{e} e-folds of inflation is a power law, P(N_{e}) \propto N_{e}^{-3}, and we derive the same exponent from a simple analytical model. The success of inflation is relatively insensitive to the initial conditions: we find attractor behavior in the angular directions, and the D3-brane can begin far above the inflection point without overshooting. In favorable regions of the parameter space, models yielding 60 e-folds of expansion arise approximately once in 10^3 trials. Realizations that are effectively single-field and give rise to a primordial spectrum of fluctuations consistent with WMAP, for which at least 120 e-folds are required, arise approximately once in 10^5 trials. The emergence of robust predictions from a six-field potential with hundreds of terms invites an analytic approach to multifield inflation.Comment: 28 pages, 9 figure