arXiv subjects

Renata Kallosh

Publications and source records attributed to Renata Kallosh.

At least 37 records · Page 2Linked to original sources

arXiv2024

Landscape of Modular Cosmology

We investigate the global structure of the recently discovered family of $SL(2,\mathbb{Z})$-invariant potentials describing inflationary $α$-attractors. These potentials have an inflationary plateau consisting of the fundamental domain and its images fully covering the upper part of the Poincaré half-plane. Meanwhile, the lower part of the half-plane is covered by an infinitely large number of ridges, which, at first glance, are too sharp to support inflation. However, we show that this apparent sharpness is just an illusion created by hyperbolic geometry, and each of these ridges is physically equivalent to the inflationary plateau in the upper part of the Poincaré half-plane.

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arXiv2024

The role of Sp(2n) duality in quantum theory

D-dimensional maximal supergravities type I with G/H coset spaces have global G-symmetry and local H symmetry, which can be gauge-fixed in symmetric or Iwasawa-type gauges. Maximal D-dimensional supergravities type II derived from higher dimensions without dualization have less local and global symmetries. In 4D, Gaillard-Zumino duality group Sp(56) enhances U-duality symmetry group $E_{7(7)}$. Using the Hamiltonian path integral, we show how extra symmetries beyond $E_{7(7)}$, serve to establish S-matrix equivalence of supergravities I and II in different gauges. Enhanced dualities are not available in D $> 4$. This is consistent with the existence of local H symmetry and global G symmetry anomalies and UV divergences in D $> 4$ supergravities, and with the absence of these anomalies and UV divergences, so far, in 4D ${\cal N}\geq 5$ supergravities.

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arXiv2024

$SL(2,\mathbb{Z})$ Cosmological Attractors

We study cosmological theory where the kinetic term and potential have $SL(2,\mathbb{Z})$ symmetry. Potentials have a plateau at large values of the inflaton field, where the axion forms a flat direction. Due to the underlying hyperbolic geometry and special features of $SL(2,\mathbb{Z})$ potentials, the theory exhibits an $α$-attractor behavior: its cosmological predictions are stable with respect to significant modifications of the $SL(2,\mathbb{Z})$ invariant potentials. We present a supersymmetric version of this theory in the framework of $\overline {D3}$ induced geometric inflation. The choice of $α$ is determined by underlying string compactification. For example, in a CY compactification with $T^2$, one has $3α=1$, the lowest discrete Poincaré disk target for LiteBIRD

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arXiv2024

Gauge-fixing local H symmetry in supergravities

We discuss known maximal D-dimensional supergravities of two types: type I with G/H coset spaces and type II derived by compactification from higher dimensions without dualization, these have less manifest symmetries. In 4D and 6D in type I models we perform explicit gauge-fixing of local H symmetries in unitary gauges: symmetric, Iwasawa, and partial Iwasawa. In 4D supergravity I in symmetric gauge global H-invariance and nonlinearly realized G-symmetry are valid on shell, classically. The global H-symmetry and G-symmetry in Iwasawa-type gauges in type I and type II supergravities are not manifest, if at all present. This fact raises the issue of the gauge equivalence of the S-matrix of various gauge-fixed D-dimensional supergravities and its relation to the ones computable using superamplitude methods.

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arXiv2024

Enhanced Duality in 4D Supergravity

U-duality imposes strong constraints on the structure of divergences in supergravity. But Gaillard-Zumino Sp$(2n_v, \mathbb{R})$ duality in D=4 has more symmetries than U-duality. For example, in $N = 8$ the dimension of Sp(56) is 1596, whereas its U-duality subgroup $E_{7(7)}$ has a dimension of 133. In comparison, in D $> 4$ maximal dualities are U-dualities. We argue that the extra dualities in 4D, enhancing U-duality, determine the properties of perturbative quantum supergravity. The presence/absence of enhanced dualities suggests a possible explanation of the results of the amplitude loop computations in D-dimensional supergravities and of the special status of D = 4 in this respect.

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arXiv2024

Ward Identities for Superamplitudes

We introduce Ward identities for superamplitudes in D-dimensional N-extended supergravities. These identities help to clarify the relation between linearized superinvariants and superamplitudes. The solutions of these Ward identities for an $n$-partice superamplitude take a simple universal form for half-BPS and non-BPS amplitudes. These solutions involve arbitrary functions of spinor helicity and Grassmann variables for each of the $n$ superparticles. The dimension of these functions at a given loop order is exactly the same as the dimension of the relevant superspace Lagrangians depending on half-BPS or non-BPS superfields, given by $(D-2) L +2- N$ or $(D-2) L +2- 2 N$, respectively. This explains why soft limits predictions from superamplitudes and from superspace linearized superinvariants agree.

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arXiv2024

Soft Theorems, Anomalies and Precursors

We find that in 6d maximal supergravity there are 3-loop order amplitudes with non-vanishing soft-scalar limits and anomalous $E_{5(5)}$ duality, induced by a 3-loop UV divergence. If the relevant non-vanishing soft-scalar limits would be detected in 1-loop amplitudes, it would be a 1-loop precursor of a 3-loop UV divergence in 6d.

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arXiv2023

Superinvariants Below Critical Loop Order

Investigation of on-shell superinvariants is the standard way to identify the candidate UV divergences in supergravity. Geometric on-shell superinvariants in 4d supergravity at $N\geq 4$ are available starting at the critical loop order. However, more than 10 years ago, it was conjectured that the UV divergences in supergravity might appear earlier, for $L=N-1$, due to the existence of harmonic superspace superinvariants based on Grassmann analytic superfields. Here we show that these harmonic superinvariants at the nonlinear level are inconsistent, because Grassmann analyticity breaks local $H$ symmetry of the $N\geq 4$ on-shell superspace. Therefore, the "puzzling enhanced cancellation" of UV divergences for $L=N-1$ in superamplitude calculations for $ L=3, \, N=4$ and $L=4, \, N=5$ is explained by nonlinear local supersymmetry consistent with unbroken local $H$ symmetry.

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arXiv2023

Hybrid $α$-attractors, primordial black holes and gravitational wave backgrounds

We investigate the two-stage inflation regime in the theory of hybrid cosmological $α$-attractors. The spectrum of inflationary perturbations is compatible with the latest Planck/BICEP/Keck results, thanks to the attractor properties of the model. However, at smaller scales, it may have a very high peak of controllable width and position, leading to a copious production of primordial black holes (PBH) and generation of a stochastic background of gravitational waves (SGWB).

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arXiv2023

Explaining enhanced UV divergence cancellations

We study supergravities with "enhanced UV divergence cancellations". We show that all these cancellations are explained by a simple dimensional analysis of nonlinear local supersymmetry (NLS). We also show that in all cases where E7-type duality was used in the past via vanishing single scalar limit (SSL) to explain/predict UV cancellations one could have used dimensional analysis of NLS. The SSL constraints predict in d=4 loop order L less or equal (N-2) for UV finiteness, dimensional analysis of NLS predicts L less or equal (N-1) for UV finiteness, including enhanced cases like N=5, L=4.

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arXiv2023

Is d=4 Maximal Supergravity Special?

We study candidate counterterms (CT)'s in maximal supergravities in diverse integer dimensions $d \geq 4 $. We find that UV divergences in these theories occur at the number of loops $L$ below certain critical value $L_{cr}$. At $L\geq L_{cr}$ the CT's have nonlinear local supersymmetry and local $H$ symmetry, but the ones below $L_{cr}$ break these symmetries. Therefore deforming the theories by adding the CT's to the action to cancel UV divergences would be inconsistent with BRST. Such divergences with $L < L_{cr}$ were found in maximal supergravities for all integer $d > 4$, but not for $N=5,6,8$ in $d = 4$ so far, which renders the case $d = 4$ special.

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arXiv2023

Deformation of d=4, N> 4 Supergravities Breaks Nonlinear Local Supersymmetry

We study d=4, $N\geq 5$ supergravities and their deformation via candidate counterterms, with the purpose to absorb UV divergences. We generalize the earlier studies of deformation and twisted self-duality constraint to the case with unbroken local H-symmetry in presence of fermions. We find that the deformed action breaks nonlinear local supersymmetry. We show that all known cases of enhanced UV divergence cancellations are explained by nonlinear local supersymmetry. This result implies, in particular, that if N=5 supergravity at five loop will turn out to be UV divergent, the deformed theory will be BRST inconsistent. If it will be finite, it will be a consequence of nonlinear local supersymmetry and E7-type duality.

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arXiv2022

Hybrid cosmological attractors

We construct $α$-attractor versions of hybrid inflation models. In these models, the potential of the inflaton field $φ$ is uplifted by the potential of the second field $χ$. This uplifting ends due to a tachyonic instability with respect to the field $χ$, which appears when $φ$ becomes smaller than some critical value $φ_{c}$. In the large $N$ limit, these models have the standard universal $α$-attractor predictions. In particular, $n_{s }= 1- {2 \over N}$ for the exponential attractors. However, in some special cases the large $N$ limit is reached only beyond the horizon, for $N \gtrsim 60$. This may change predictions for the cosmological observations. For any fixed $N$, in the limit of large uplift $V_{\rm up}$, or in the limit of large $φ_{c}$, we find another attractor prediction, $ n_s = 1$. By changing the parameters $V_{\rm up}$ and $φ_{c}$ one can continuously interpolate between the two attractor predictions $n_{s }= 1- {2 \over N}$ and $n_{s} = 1$. This provides significant flexibility, which can be very welcome in view of the rapidly growing amount and precision of the cosmological data. Our main result is not specific to the hybrid inflation models. Rather, it is generic to any inflationary models where the inflaton potential, for some reasons, is uplifted, and inflation ends prematurely.

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arXiv2022

Goldstino Condensation?

It was argued in \cite{DallAgata:2022abm} that the Volkov-Akulov (VA) model as well as similar models in supergravity and the related KKLT model in string theory, suffer from tachyonic instabilities due to goldstino condensation. The authors of \cite{DallAgata:2022abm} constructed a specific model with two unconstrained interacting chiral superfields with linearly realized supersymmetry which has an unstable vacuum. They claimed that this model becomes equivalent to the VA model in the UV limit. We show that the UV limit of their model is discontinuous, and the vacuum instability of the model proposed in \cite{DallAgata:2022abm} is not relevant to the VA model, to related models in supergravity, and to the KKLT construction.

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arXiv2022

Dilaton-Axion Inflation with PBHs and GWs

We discuss two-stage dilaton-axion inflation models [1] and describe $α$-attractor models with either exponential or polynomial approach to the plateau. We implement one of the models of primordial black hole production proposed in [2] in the $α$-attractor context, and develop its supergravity version. The predictions of this model following from its polynomial attractor properties are: $n_s$ and $r$ are $α$-independent, $r$ depends on the mass parameter $μ$ defining the approach to the plateau. The tachyonic instability at the transition point between the two stages of inflation is proportional to the negative curvature of the hyperbolic space $\mathcal{R}_K=-2/3α$. Therefore the masses of primordial black holes (PBHs) and the frequencies of small-scale gravitational waves (GWs) in this model show significant dependence on $α$.

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arXiv2022

Polynomial $α$-attractors

Inflationary $α$-attractor models can be naturally implemented in supergravity with hyperbolic geometry. They have stable predictions for observables, such as $n_s=1-{2/ N_e} $, assuming that the potential in terms of the original geometric variables, as well as its derivatives, are not singular at the boundary of the hyperbolic disk, or half-plane. In these models, the potential in the canonically normalized inflaton field $φ$ has a plateau, which is approached exponentially fast at large $φ$. We call them exponential $α$-attractors. We present a closely related class of models, where the potential is not singular, but its derivative is singular at the boundary. The resulting inflaton potential is also a plateau potential, but it approaches the plateau polynomially. We call them polynomial $α$-attractors. Predictions of these two families of attractors completely cover the sweet spot of the Planck/BICEP/Keck data. The exponential ones are on the left, the polynomial are on the right.

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arXiv2021

BICEP/Keck and Cosmological Attractors

We discuss implications of the latest BICEP/Keck data release for inflationary models, with special emphasis on the cosmological attractors which can describe all presently available inflation-related observational data. These models are compatible with any value of the tensor to scalar ratio $r$, all the way down to $r = 0$. Some of the string theory motivated models of this class predict $10^{-3} \leq r \leq 10^{-2}$. The upper part of this range can be explored by the ongoing BICEP/Keck observations.

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arXiv2021

CMB targets after the latest Planck data release

We show that a combination of the simplest $α$-attractors and KKLTI models related to Dp-brane inflation covers most of the area in the ($n_{s}$, $r$) space favored by Planck 2018. For $α$-attractor models, there are discrete targets $3α=1,2,...,7$, predicting 7 different values of $r = 12α/N^{2}$ in the range $10^{-2} \gtrsim r \gtrsim 10^{-3}$. In the small $r$ limit, $α$-attractors and Dp-brane inflation models describe vertical $β$-stripes in the ($n_{s}$, $r$) space, with $n_{s}=1-β/N$, $β=2, {5\over 3},{8\over 5}, {3\over 2},{4\over 3}$. A phenomenological description of these models and their generalizations can be achieved in the context of pole inflation. Most of the $1σ$ area in the ($n_{s}$, $r$) space favored by Planck 2018 can be covered models with $β= 2$ and $β= 5/3$. Future precision data on $n_s$ may help to discriminate between these models even if the precision of the measurement of $r$ is insufficient for the discovery of gravitational waves produced during inflation.

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