The exact localization result for the expectation value of the <math altimg='si1.svg'><mfrac><mn>1</mn><mn>2</mn></mfrac></math> BPS circular Wilson loop in <math altimg='si2.svg'><mrow><mi mathvariant='script'>N</mi><mo linebreak='goodbreak'>=</mo><mn>4</mn></mrow></math> SYM theory is given in the planar limit by the famous Bessel function expression: <math altimg='si3.svg'><mrow><mrow><mo>&#9001;</mo><mi>W</mi><mo>&#9002;</mo></mrow><mo linebreak='goodbreak'>=</mo><mfrac><mrow><mn>2</mn><mi>N</mi></mrow><msqrt><mi>&#955;</mi></msqrt></mfrac><msub><mi>I</mi><mn>1</mn></msub><mrow><mo>(</mo><msqrt><mi>&#955;</mi></msqrt><mo>)</mo></mrow></mrow></math>. Expanded in large <italic>&#955;</italic> and expressed in terms of the AdS <inf>5</inf>&#8239;&#215;&#8239; <italic>S</italic> 5 string tension <math altimg='si4.svg'><mrow><mi>T</mi><mo linebreak='goodbreak'>=</mo><mfrac><msqrt><mi>&#955;</mi></msqrt><mrow><mn>2</mn><mi>&#960;</mi></mrow></mfrac></mrow></math> this gives <math altimg='si5.svg'><mrow><mrow><mo>&#9001;</mo><mi>W</mi><mo>&#9002;</mo></mrow><mo linebreak='goodbreak'>=</mo><mfrac><msqrt><mi>T</mi></msqrt><mrow><mn>2</mn><mi>&#960;</mi><msub><mi>g</mi><mi>s</mi></msub></mrow></mfrac><msup><mi>e</mi><mrow><mn>2</mn><mi>&#960;</mi><mi>T</mi></mrow></msup><mrow><mo>(</mo><mn>1</mn><mo linebreak='badbreak'>&#8722;</mo><mfrac><mn>3</mn><mrow><mn>16</mn><mi>&#960;</mi></mrow></mfrac><msup><mi>T</mi><mrow><mo>&#8722;</mo><mn>1</mn></mrow></msup><mo linebreak='badbreak'>+</mo><mo>&#8230;</mo><mo>)</mo></mrow></mrow></math>.The exponential is matched by the value of the action of the string with the AdS <inf>2</inf> world volume while the prefactor comes from the 1-loop GS string correction. Here we address the question of how the subleading <math altimg='si6.svg'><msup><mi>T</mi><mrow><mo>&#8722;</mo><mn>1</mn></mrow></msup></math> term could be reproduced by the 2-loop correction in the corresponding partition function of the AdS <inf>5</inf>&#8239;&#215;&#8239; <italic>S</italic> 5 GS string expanded near the AdS <inf>2</inf> minimal surface. We find that the string correction contains a non-zero UV logarithmic divergence implying that comparison with the SYM result requires a particular subtraction prescription. We discuss implications of this conclusion for checking the AdS/CFT duality at strong coupling.

Italy

M. Beccaria

United Kingdom

S.A. Kurlyand

A.A. Tseytlin

Strong coupling expansion of <math altimg='si1.svg'><mfrac><mn>1</mn><mn>2</mn></mfrac></math> BPS Wilson loop in SYM theory and 2-loop Green-Schwarz string in AdS <inf>5</inf>&#8239;&#215;&#8239; <italic>S</italic> 5

We show that the gravitational Green-Schwarz (GS) transformation becomes trivial in the nonrelativistic (NR) limit of ten-dimensional heterotic supergravity with four-derivative corrections. This constitutes an important step towards establishing the trivialization of the GS mechanism in this limit. In this work, we perform a NR expansion of the Kalb-Ramond field and identify the finite Green-Schwarz transformation in this limit, which can be interpreted as a noncovariant <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi><mi>O</mi><mo stretchy="false">(</mo><mn>8</mn><mo stretchy="false">)</mo></math> transformation. We then construct an explicit field redefinition such that the redefined two-form is invariant under this symmetry. This result is compared with the previously reported trivialization of the gauge GS mechanism under the same limit. Both field redefinitions can be implemented simultaneously, and the associated Chern-Simons terms are exact, arising directly from the redefinition structure, and leading to a trivial Bianchi identity. These results support the expectation that anomaly cancellation becomes automatic in the NR regime, and therefore we discuss their potential implications.

Poland

Eric Lescano

Trivialization of the gravitational Green-Schwarz transformation in the nonrelativistic limit of string theory

Compatibility with T-duality severely constrains higher-derivative corrections to the low-energy supergravity limits of string theory. For example, it suggests that Lorentz transformations for heterotic strings are modified in precisely the way required for the Green-Schwarz anomaly cancellation mechanism. A systematic procedure to construct the resulting generalized Green-Schwarz transformations is the generalized Bergshoeff-de Roo identification (gBdRi) <a href="http://dx.doi.org/10.1007/JHEP11(2018)160">J. High Energy Phys. 11 (2018) 160</a>; <a href="http://dx.doi.org/10.1007/JHEP01(2021)171">J. High Energy Phys. 01 (2021) 171</a>. Although it in principle allows computing <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>α</mi><mo>′</mo></msup></math>-corrections to higher and higher orders, technically it becomes unfeasible beyond <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mrow><mi>α</mi></mrow><mrow><mo>′</mo><mn>2</mn></mrow></msup></math>. We revisit this problem with an alternative approach to the gBdRi, which we have recently developed. It gives rise to a very simple all-order transformation law whose closure we verify by explicitly computing the resulting gauge algebra.

Achilleas Gitsis

Falk Hassler

All-order generalized Green-Schwarz transformations

It is well-known that a Lagrangian resembling scalar–tensor gravity naturally emerges from string theory in the low-energy limit. This suggests that a scalar–tensor theory intrinsically inhabits precious information about quantum gravitational effects. With this motivation, we quantize the scalar–tensor theory $$R+ \lambda R\phi ^2$$ in order to unfold the black hole physics in quantum gravity. We are interested in the behavior of the wave function near the interior singularity of a black hole, which would give a pathway to resolving the singularity. Consequently, we employ canonical quantization in a Kantowski–Sachs minisuperspace representation for the black hole interior. The ensuing Wheeler–DeWitt equation turns out to be intricately coupled among the three minisuperspace variables. Upon a suitable transformation, one of the variables could be easily separated – however, the scalar field $$\phi $$ remains coupled intricately and cannot be separated by any obvious transformation. Consequently, we employ a perturbative approach in powers of $$\lambda $$ . As a result, the zeroth order equation is immediately separable, and the first order equation still remains coupled in two variables. We adopt a Green function approach to solve this first order (inhomogeneous) equation. Our detailed calculation reveals that the Green function is well-defined in the vicinity of the black hole singularity, an important result for admitting the DeWitt criterion for singularity resolution. Furthermore, our calculations illustrate that both the zeroth order and first order wave functions are well-defined at the singularity as they are consistent with the DeWitt criterion, paving the way to black hole singularity resolution in scalar–tensor quantum gravity.

India

Harpreet Singh

Malay Nandy

Quantum black holes in scalar–tensor gravity: a Green function approach

The conservation of the long wavelength fluctuations of the metric plays a vital role in cosmology as the link between quantum fluctuations during inflation and late time observations. This is a well-known property of the classical evolution equations, but demonstrating that it is robust to quantum correction involves a number of technical arguments. In this paper, we will use effective field theory (EFT) techniques to demonstrate the all orders conservation of the superhorizon scalar and tensor fluctuations of the metric during inflation. We show how to construct an EFT for these soft modes, in analogy with soft de Sitter effective theory. We pay particular attention to how the breaking of time diffeomorphisms by the inflationary background introduces new timescales that alter the structure of the EFT. In this description, the all orders conservation of the metric fluctuations is a direct consequence of symmetries and power counting that cannot be altered by loop corrections. We further show that this holds when the inflaton (or metric fluctuations) is coupled to additional heavy fields, as in quasi-single-field inflation. We match this behavior to several calculations in the ultraviolet (UV) theory and show how the Mellin representation enables a more transparent connection between the UV and the EFT descriptions.

United States

Daniel Green

Kshitij Gupta

Soft metric fluctuations during inflation

The late-time limit of the power spectrum for heavy (principal series) fields in de Sitter (dS) space yields a series of polynomial terms with complex scaling dimensions. Such scaling behavior is expected to result from an associated operator with a complex dimension. In a free theory, these complex dimensions are known to match the constraints imposed by unitarity on the space of states. Yet, perturbative corrections to the scaling behavior of operators are naively inconsistent with unitary evolution of the quantum fields in dS space. This paper demonstrates how to compute one-loop corrections to the scaling dimensions that appear in the two-point function from the field theory description in terms of local operators. We first show how to evaluate these anomalous dimensions using Mellin space, which has the feature that it naturally accommodates a scaleless regulator. We then explore the consequences for the soft de Sitter effective theory (SdSET) description that emerges in the long wavelength limit. Carefully matching between the UV and SdSET descriptions requires the introduction of novel nondynamical “operators” in the effective theory. This is not only necessary to reproduce results extracted from the Källén-Lehmann representation (that use the space of unitary states directly), but it is also required by general arguments that invoke positivity.

CERN

Switzerland

Timothy Cohen

Yiwen Huang

Operator origin of anomalous dimensions in de Sitter space

The predictions of inflation are usually defined in terms of equal time in-in correlation functions in an accelerating cosmological background. These same observables exist for quantum field theory in other spacetimes, including flat space. In this paper, we will explore how the Wilsonian renormalization group (RG) and effective field theory (EFT) apply to these observables in both flat and de Sitter space. Specifically, we show that matching the short- and long-distance calculations requires additional terms localized at the time of the measurement that are not captured by the effective action of the EFT. These additional terms only correct the local and semi-local terms in the EFT correlators. In flat space, we give an explicit demonstration by matching in-in correlators of light scalars interacting with a heavy field with the EFT result. We then show how these additional terms arise generically via exact RG. We also compare these explicit results in flat space with the corresponding theory in de Sitter and show that the local terms typically redshift away. Our results are closely related to momentum space entanglement that arises from tracing over short-wavelength modes.

Guanhao Sun

Effective field theory and in-in correlators

The electrical conductivity of hot and dense quark matter is calculated using the 2-flavour gauged Nambu–Jona–Lasinio (NJL) model in the presence of a chiral imbalance quantified in terms of a chiral chemical potential (CCP). To this end, the in-medium spectral function corresponding to the vector current correlator is evaluated employing the real time formulation of finite temperature field theory. Taking the long wavelength limit of the spectral function we extract the electrical conductivity using the Green–Kubo relation. The thermal widths of the quarks/antiquarks that appear in the expression of electrical conductivity are calculated by considering the $$2\rightarrow 2$$ scattering in the NJL model. The scattering amplitudes containing the polarization functions of the mesonic modes in the scalar and pseudoscalar channels are also evaluated by considering finite value of CCP. We find that the ratio of electrical conductivity to temperature has significant dependence on CCP especially in the low temperature region.

Snigdha Ghosh

Nilanjan Chaudhuri

Sourav Sarkar

Pradip Roy

Effect of chiral imbalance on the electrical conductivity of hot and dense quark matter using Green–Kubo method within the 2-flavour gauged NJL model

The effective field theory of single-field inflation characterizes the inflationary epoch in terms of a pattern of symmetry breaking. An operator acquires a time-dependent vacuum expectation value, defining a preferred spatial slicing. In the absence of dynamical gravity, the fluctuations around the time-dependent background are described by the Goldstone boson associated with this symmetry breaking process. With gravity, the Goldstone is eaten by the metric, becoming the scalar metric fluctuation. In this paper, we will show that in general single-field inflation, the statistics of scalar metric fluctuations are given by the statistics of this Goldstone boson decoupled from gravity up to corrections that are controlled as an expansion in slow-roll parameters. This even holds in the presence of additional parameters, like the speed of sound, that naively enhance the impact of the gravitational terms. In the process, we derive expressions for leading and sub-leading gravitational corrections to all-orders in the Goldstone boson.

A Goldstone boson equivalence for inflation

The baryon acoustic oscillation (BAO) analysis from the first year of data from the Dark Energy Spectroscopic Instrument (DESI), when combined with data from the cosmic microwave background (CMB), has placed an upper-limit on the sum of neutrino masses, ∑m  ν  &lt; 70 meV (95%). In addition to excluding the minimum sum associated with the inverted hierarchy, the posterior is peaked at ∑m  ν  = 0 and is close to excluding even the minumum sum, 58 meV at 2σ. In this paper, we explore the implications of this data for cosmology and particle physics. The sum of neutrino mass is determined in cosmology from the suppression of clustering in the late universe. Allowing the clustering to be enhanced, we extended the DESI analysis to ∑m  ν  &lt; 0 and find ∑m  ν  =160±90 meV (68%), and that the suppression of power from the minimum sum of neutrino masses is excluded at 99% confidence. We show this preference for negative masses makes it challenging to explain the result by a shift of cosmic parameters, such as the optical depth or matter density. We then show how a result of ∑m  ν  = 0 could arise from new physics in the neutrino sector, including decay, cooling, and/or time-dependent masses. These models are consistent with current observations but imply new physics that is accessible in a wide range of experiments. In addition, we discuss how an apparent signal with ∑m  ν  &lt; 0 can arise from new long range forces in the dark sector or from a primordial trispectrum that resembles the signal of CMB lensing.