A measurement of correction factors for the hadronic jet energy scale and resolution in the ATLAS detector is presented. These correction factors account for differences between simulated and observed data. They are obtained by analysing a selection of top quark events collected in proton–proton collisions by ATLAS between the years 2015 and 2018 at a centre-of-mass energy $$\sqrt{s} = 13$$ $$\text {T{eV}}$$ as well as in 2022 and 2023 at $$\sqrt{s} = 13.6$$ $$\text {T{eV}}$$ . The impact of different jet energy scale or resolution corrections on the reconstructed mass of the hadronically decaying $\textit{W}$ boson from top-quark decays in simulation is quantified. The correction factors are extracted from a fit to the parameterised reconstructed $\textit{W}$-boson mass distribution to data. The energy scale and resolution corrections are measured as a function of the jet transverse momentum between 20 and 200 GeV and absolute pseudorapidity less than 0.8. The uncertainties in the energy scale range from about 0.93% to about 1.7% for jets between 35 and 200 $$\text {G{eV}}$$ , while for the energy resolution the uncertainties range from about 14 to 28%. The method presented will be used in conjunction with other techniques to further improve ATLAS jet energy scale and resolution precision.

France

G. Aad

Norway

E. Aakvaag

United States

B. Abbott

United Arab Emirates

S. Abdelhameed

Germany

K. Abeling

N. Abicht

S. Abidi

M. Aboelela

Morocco

A. Aboulhorma

Israel

H. Abramowicz

Italy

United Kingdom

B. Acharya

A. Ackermann

C. Bourdarios

Poland

L. Adamczyk

S. Addepalli

M. Addison

J. Adelman

Türkiye

A. Adiguzel

T. Adye

A. Affolder

Y. Afik

Spain

M. Agaras

A. Aggarwal

Romania

C. Agheorghiesei

Azerbaijan

F. Ahmadov

S. Ahuja

China

X. Ai

G. Aielli

A. Aikot

M. Tamlihat

B. Aitbenchikh

Sweden

T. Åkesson

Japan

D. Akiyama

N. Akolkar

S. Aktas

G. Alberghi

Canada

J. Albert

Switzerland

U. Alberti

P. Albicocco

G. Albouy

S. Alderweireldt

Z. Alegria

M. Aleksa

I. Aleksandrov

C. Alexa

Greece

T. Alexopoulos

F. Alfonsi

M. Algren

M. Alhroob

Czechia

B. Ali

Saudi Arabia

H. Ali

S. Ali

S. Alibocus

South Africa

M. Aliev

G. Alimonti

W. Alkakhi

C. Allaire

B. Allbrooke

D. Allen

J. Allen

Australia

C. Alley

A. Aloisio

Argentina

F. Alonso

C. Alpigiani

Z. Alsolami

A. Fernandez

M. Cardoso

M. Alviggi

M. Aly

Brazil

Y. Coutinho

A. Ambler

C. Amelung

M. Amerl

T. Amezza

B. Amini

K. Amirie

A. Amirkhanov

Portugal

S. Santos

D. Amperiadou

S. An

C. Anastopoulos

T. Andeen

J. Anders

A. Anderson

A. Andreazza

S. Angelidakis

A. Angerami

A. Anisenkov

A. Annovi

C. Antel

E. Antipov

M. Antonelli

F. Anulli

M. Aoki

T. Aoki

M. Aparo

L. Bella

M. Apicella

Calibration of the jet energy scale and resolution of small-radius jets using semileptonic $$t\bar{t}$$ events with the ATLAS detector

We discuss the reconstruction of scalar field potential necessary to witness inflation at the very early phase of the Universe. A minimally coupled inflaton field is considered along with a modified teleparallel gravity where the action contains a function of torsion. Reconstruction mechanism in a most general way is discussed. Constant roll inflation is imposed upon the field equations to simplify the reconstruction procedure. Considering a functional form of $\textit{f}$($\textit{T}$), we obtained the effective scalar field potential and Hubble parameter in an analytic manner.

India

B. Mishra

S. Tripathy

Constant roll inflation and reconstruction of scalar field potential in $\textit{f}$($\textit{T}$) gravity

<list id='lst0001'><list-item id='lstitem0001'><label>&#8226;</label><para id='p0001'>MSSM-like spectra are constructed from magnetized 7-brane configurations.</para></list-item><list-item id='lstitem0002'><label>&#8226;</label><para id='p0002'>Semi-realistic quark and charged-lepton flavor structures are realized from wavefunction overlaps.</para></list-item><list-item id='lstitem0003'><label>&#8226;</label><para id='p0003'>Exotic matter zero-modes are eliminated.</para></list-item><list-item id='lstitem0004'><label>&#8226;</label><para id='p0004'>Additional 7-branes are systematically embedded as sequestered hidden sectors.</para></list-item></list>

Hiroyuki Abe

Molin Chen

Itsuki Miyane

Naoki Shimada

MSSM flavors from 7-brane configurations of magnetized SYM on <math altimg='si39.svg'><mrow><msup><mi>R</mi><mrow><mn>1</mn><mo>,</mo><mn>3</mn></mrow></msup><mo linebreak='goodbreak'>&#215;</mo><msup><mrow><mo>(</mo><msup><mi>T</mi><mn>2</mn></msup><mo>)</mo></mrow><mn>3</mn></msup><mo linebreak='goodbreak'>/</mo><mrow><mo>(</mo><msub><mi>Z</mi><mn>2</mn></msub><mo linebreak='badbreak'>&#215;</mo><msubsup><mi>Z</mi><mn>2</mn><mo>&#8242;</mo></msubsup><mo>)</mo></mrow></mrow></math>

In this work, we investigate the cosmological consequences of an effective ΛCDM model emerging from the more general <italic>f</italic>( <italic>Q, T</italic>) gravity theory under the special equation-of-state condition <math altimg='si20.svg'><mrow><mi>&#961;</mi><mo linebreak='goodbreak'>+</mo><mi>p</mi><mo linebreak='goodbreak'>=</mo><mn>0</mn></mrow></math>. Under this limit, the field equations yield the constraint <math altimg='si21.svg'><mrow><mi>F</mi><mo>(</mo><mi>Q</mi><mo>,</mo><mi>T</mi><mo>)</mo><mi>H</mi><mo>(</mo><mi>t</mi><mo>)</mo><mo>=</mo><mi>C</mi></mrow></math>, implying that the function <math altimg='si22.svg'><mrow><mi>F</mi><mo linebreak='goodbreak'>=</mo><msub><mi>f</mi><mi>Q</mi></msub></mrow></math> becomes purely dependent on the non-metricity scalar <italic>Q</italic>, and the background evolution mimics that of the standard &#923;CDM model. We derive the resulting functional forms of <italic>f</italic>( <italic>Q</italic>), obtain the corresponding effective cosmological constant, and analyze the physical nature of this reduction. To test the model against observations, we perform a background-level parameter estimation for <italic>H</italic> <inf>0</inf> and &#937; <inf><italic>m</italic></inf>, and evaluate the derived parameter <italic>S</italic> <inf>8</inf> (anchored to the Planck baseline <italic>&#963;</italic> <inf>8</inf>) using cosmic chronometers (CC), baryon acoustic oscillations (BAO), and Pantheon+ SN Ia datasets. A dual-pipeline analysis is carried out using conventional Bayesian Markov Chain Monte Carlo (MCMC) sampling alongside a machine-learning based Artificial Neural Network (ANN) emulator deployed as a complementary consistency check. We demonstrate that the ANN approach successfully emulates the continuous parameter space with high computational efficiency, yielding results in close agreement with the standard MCMC likelihood framework. Because the background evolution strictly mimics the standard &#923;CDM paradigm, the model successfully reproduces recent observational trends and recovers standard parameter constraints without dynamically resolving the baseline <italic>H</italic> <inf>0</inf> and <italic>S</italic> <inf>8</inf> tensions. Our results indicate that effective &#923;CDM scenarios derived from <italic>f</italic>( <italic>Q, T</italic>) gravity provide a viable and consistent with recent observational data.

Anil Kumar Yadav

S.H. Shekh

Kazakhstan

N. Myrzakulov

Anirudh Pradhan

Nafis Ahmad

A.M. Alshehri

Effective ΛCDM model emerging from <italic>f</italic>( <italic>Q, T</italic>) under a special EOS limit in symmetric cosmology with Bayesian and ANN observational constraints

Understanding near-threshold strong interactions is essential for disentangling hadronic molecules and compact multiquark states in heavy-flavor spectroscopy. In this context, the doubly charmed tetraquark candidate <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow></msub><mo stretchy="false">(</mo><mn>3875</mn><msup><mo stretchy="false">)</mo><mo>+</mo></msup></math> serves as a critical benchmark because it lies very close to the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>D</mi><mo>*</mo></msup><mo>−</mo><mi>D</mi></math> thresholds. Motivated by the interaction ambiguity reported recently [<a href="http://dx.doi.org/10.1103/kd4s-9rzr">Phys. Rev. D 113, L031505 (2026)</a>], we evaluate the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>D</mi><mo>*</mo></msup><mo>−</mo><mi>D</mi></math> scattering lengths and femtoscopic correlation functions for the molecular and molecule-compact admixture assignments of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow></msub><mo stretchy="false">(</mo><mn>3875</mn><msup><mo stretchy="false">)</mo><mo>+</mo></msup></math>. We show that, although these scenarios yield similar invariant-mass line shapes, their corresponding femtoscopic correlation functions differ markedly and remain clearly distinguishable for typical particle-emitting sources created at the LHC. Our results indicate that femtoscopy can serve as a sensitive and complementary probe of the near-threshold dynamics of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow></msub><mo stretchy="false">(</mo><mn>3875</mn><msup><mo stretchy="false">)</mo><mo>+</mo></msup></math>, providing vital theoretical references for future LHC femtoscopy measurements.

Duo-Lun Ge

Zhi-Wei Liu

Li-Sheng Geng

<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>D</mi><msup><mrow><mi>D</mi></mrow><mrow><mo>*</mo></mrow></msup></mrow></math> correlation functions in deciphering the nature of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow></msub><mo stretchy="false">(</mo><mn>3875</mn><msup><mo stretchy="false">)</mo><mo>+</mo></msup></math>

We study self-dual instantons of topological charge $$ Q=\frac{r}{N} $$ , ∀$\textit{r}$ ∈ $\textit{ℕ}$, in $\textit{SU}$ ($\textit{N}$) Yang-Mills theory on $$ {\mathbbm{T}}^4 $$ with ’t Hooft twists, by embedding them into worldvolume theories of $\textit{D}$-branes. To study their moduli, we construct the wrapped intersecting brane configurations dual to general constant field strength instanton backgrounds. We show that, locally, the moduli space is identified with the Higgs branch of an $$ \mathcal{N} $$ =2 supersymmetric theory. This parameterization of the moduli space is equivalent to one recently found in field theory, but is obtained with significantly less effort and has manifest hyper-Kähler structure. Our hope is that combining different perspectives on instantons on the twisted torus will help understand the still unknown global structure of the moduli space for general solutions with $$ Q=\frac{r}{N} $$ as well as the nature of instantons with all moduli turned on — when some $\textit{Q}$<1 and all $\textit{Q}$≥1 instantons become space-time dependent. For integer $\textit{Q}$, these are expected to match the ADHM solution in an appropriately taken infinite volume limit.

Erich Poppitz

$\textit{D}$-branes and fractional instantons on a twisted $$ {\mathbbm{T}}^4 $$ : the moduli space as an $$ \mathcal{N} $$ = 2 supersymmetric Higgs branch

Motivated by the recent observation of the pseudoscalar toponium $${\eta }_{t}$$ at the LHC and by the ongoing interest in its properties, we phenomenologically investigate the $${\eta }_{t}$$ $${\rightarrow }$$ $$W^{+}W^{-}$$ process, one of the characteristic decays of toponium $${\eta }_{t}$$ . The branching ratio for the $${\eta }_{t}$$ $${\rightarrow }$$ $$W^{+}W^{-}$$ decay is estimated with two scenarios of the decay constant $$f_{{\eta }_{t}}$$ . It is found that tens of dilepton events from the cascade decays, $${\eta }_{t}$$ $${\rightarrow }$$ $$W^{+}W^{-}$$ $${\rightarrow }$$ $${\ell }^{-}\bar{\nu }_{\ell }{\ell }^{{\prime }+}{\nu }_{{\ell }^{\prime }}$$ with $${\ell }$$ , $${\ell }^{\prime }$$ $$=$$ $\textit{e}$ and $${\mu }$$ , could be experimentally observed, when considering the realistic identification efficiency of the charged lepton and assuming more than $$3{\times }10^{7}$$ $${\eta }_{t}$$ events available at the future HL-LHC. We propose searching for $${\eta }_{t}$$ via the $${\eta }_{t}$$ $${\rightarrow }$$ $$W^{+}W^{-}$$ $${\rightarrow }$$ $${\ell }^{-}\bar{\nu }_{\ell }{\ell }^{{\prime }+}{\nu }_{{\ell }^{\prime }}$$ channel, which features no $\textit{b}$-jets and clean dilepton signatures, thus offering a complementary and potentially more sensitive probe.

Yueling Yang

Bingbing Yang

Junfeng Sun

Prospects for observing the $${\eta }_{t}$$ $${\rightarrow }$$ $$W^{+}W^{-}$$ decay at the HL-LHC

The doubly charmed tetraquark <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow></msub></math> was reported by the LHCb experiment in 2022 and a lot of theoretical studies have been conducted. The small binding energy measured from the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>D</mi><mrow><mo>*</mo><mo>+</mo></mrow></msup><msup><mi>D</mi><mn>0</mn></msup></math> threshold indicates that <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow></msub></math> is a <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><msup><mi>D</mi><mo>*</mo></msup></math> molecule. On the other hand, the superflavor symmetry, which relates heavy antiquarks to heavy diquarks, provides a useful framework for predicting the existence of partner exotic hadrons associated with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow></msub></math>. By replacing <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msup></math> with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Ξ</mi><mrow><mi>c</mi><mi>c</mi></mrow><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msubsup></math> within this symmetry, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msup><msubsup><mi mathvariant="normal">Ξ</mi><mrow><mi>c</mi><mi>c</mi></mrow><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msubsup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Ξ</mi><mrow><mi>c</mi><mi>c</mi></mrow><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msubsup><msubsup><mi mathvariant="normal">Ξ</mi><mrow><mi>c</mi><mi>c</mi></mrow><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msubsup></math> are expected to form partner structures of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow></msub></math>. In this paper, we investigate bound and resonant states of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msup><msubsup><mi mathvariant="normal">Ξ</mi><mrow><mi>c</mi><mi>c</mi></mrow><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msubsup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Ξ</mi><mrow><mi>c</mi><mi>c</mi></mrow><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msubsup><msubsup><mi mathvariant="normal">Ξ</mi><mrow><mi>c</mi><mi>c</mi></mrow><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msubsup></math> based on the one boson exchange potential, where <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>π</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ρ</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ω</mi></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>σ</mi></math> are considered as bosons. The cutoff parameter and the coupling constants for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msup><msubsup><mi mathvariant="normal">Ξ</mi><mrow><mi>c</mi><mi>c</mi></mrow><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msubsup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Ξ</mi><mrow><mi>c</mi><mi>c</mi></mrow><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msubsup><msubsup><mi mathvariant="normal">Ξ</mi><mrow><mi>c</mi><mi>c</mi></mrow><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msubsup></math> are taken to be the same as those for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow></msub></math> due to superflavor symmetry. We also discuss the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>σ</mi></math> coupling constant, which is uncertain, dependence of these mass spectra. A lot of bound and resonant states with some quantum numbers are obtained for each <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>σ</mi></math> coupling constant, but these mass spectra depend on the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>σ</mi></math> coupling constant significantly.

Manato Sakai

Yasuhiro Yamaguchi

Possible <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mover accent="true"><mrow><mi>D</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover></mrow><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msup><msubsup><mrow><mi mathvariant="normal">Ξ</mi></mrow><mrow><mi>c</mi><mi>c</mi></mrow><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msubsup></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msubsup><mrow><mi mathvariant="normal">Ξ</mi></mrow><mrow><mi>c</mi><mi>c</mi></mrow><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msubsup><msubsup><mrow><mi mathvariant="normal">Ξ</mi></mrow><mrow><mi>c</mi><mi>c</mi></mrow><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msubsup></mrow></math> molecules as superflavor partners of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow></msub></math>

We perform a data-driven study of the doubly charmed tetraquark candidate <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow><mo>+</mo></msubsup></math>. An ensemble of deep neural network classifiers, trained on synthetic amplitudes with controlled analytic structures, identifies a dominant pole topology characterized by an isolated pole on the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">[</mo><mi>b</mi><mi>t</mi><mo stretchy="false">]</mo></math> Riemann sheet which is robust against left-hand cut effects. A subsequent pole parameter extraction was performed via the uniformized <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">S</mi></math>-matrix and a complementary <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">K</mi></math>-matrix parametrization, which respectively provides a model-independent baseline and dynamical insight on the pole position and trajectory of the resonant state. Using this two-pronged approach, we submit that the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow><mo>+</mo></msubsup></math> is a shallow <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>D</mi><mn>0</mn></msup><msup><mi>D</mi><mrow><mo>*</mo><mo>+</mo></mrow></msup></math> bound state in the second Riemann sheet of the complex plane.

Philippines

Julius B. Pagayon

Klarence Tomas R. Cervantes

Denny Lane B. Sombillo

Deep learning topological inference-guided <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msubsup><mrow><mi>T</mi></mrow><mrow><mi>c</mi><mi>c</mi></mrow><mrow><mo>+</mo></mrow></msubsup></mrow></math> pole parameter extraction

We perform three T-dualities on classical $$ \mathcal{N} $$ = 1 scale-separated AdS solutions of massive type IIA supergravity. These solutions arose from a compactification on a toroidal $\textit{G}$ -holonomy space with smeared O2 and O6/D6 sources. The T-dual backgrounds are classical $$ \mathcal{N} $$ = 1 AdS solutions of type IIB supergravity with O5/D5 and O9/D9 sources (type I) compactified on a space with $\textit{G}$ -structure and non-vanishing Ricci scalar. We generalize the original solutions in IIA in the T-dual picture and present on the type IIB side fully classical solutions with parametric control, scale separation, and integer conformal dimensions for the dual operators in the corresponding CFT. We also obtain strongly coupled solutions with the same properties. These are S-dual to parametrically controlled classical solutions of the heterotic SO(32) string theory.