arXiv subjects

E. H Saidi

Publications and source records attributed to E. H Saidi.

At least 19 recordsLinked to original sources

arXiv2026

Algebraic constructions of code lattices in Narain conformal field theories

We give new results on the structure and representations of the three lattices $\mathbf{Λ}_{\mathrm{k}},\mathbf{Λ}_{\mathrm{k}\mathcal{C}},\mathbf{Λ}_{\mathrm{k}}^{\ast }$ relevant to code CFTs realizing Narain conformal field theories. In this construction, $\mathbf{Λ}_{\mathrm{k}}^{\ast }$ denotes the dual of the even lattice $\mathbf{Λ}_{\mathrm{k}}$ and $\mathbf{Λ}_{\mathrm{k}\mathcal{C}}$ is an even self-dual intermediate lattice with a (d,d) signature. We study the inclusion relations $\mathbf{Λ}_{\mathrm{k}}\subset \mathbf{Λ} _{\mathrm{k}\mathcal{C}}\subset \mathbf{Λ}_{\mathrm{k}}^{\ast }$ characterized by the discriminant group $\mathbf{Λ} _{\mathrm{k}}^{\ast }/\mathbf{Λ}_{\mathrm{k}}$ isomorphic to $\mathbb{Z}_{\mathrm{k}}$ and provide explicit constructions of these $\mathbb{R}^{(\mathrm{r}d,\mathrm{r}d)}$ lattices first for rank $\mathrm{r}=d=1$ and then for higher dimensional Lie algebras with $\mathrm{r}=d>1$. Additional structural features and generalisations are also discussed.

hep-th↗

arXiv2025

Landscape of Narain CFTs

In this work, we investigate the AdS$_{3}$ gravitational bulk dual to an ensemble of Narain CFTs and their generalisations to establish bounds consistent with the Swampland program. Focusing on the AdS distance and finiteness conjectures, we show that the central charge of Narain CFTs forming the ensemble must be finite. Combining anomaly and unitary requirements, we derive an upper bound on the rank of the abelian U(1) gauge symmetries that can consistently couple to the AdS$_{3}$ gravity. We give explicit realisations of these constraints by determining the range of the Chern-Simons level $k^{G}$ corresponding to a bounded AdS$_{3}$ radius$.$ Accordingly, the Narain landscape is finite with a number of admissible CFTs constrained as $3/2\lesssim c\lesssim 10^{3}.$

hep-th↗

arXiv2025

Code CFTs and Topological Matter

In this paper, we propose a novel framework for modeling topological phases of matter using code-based Narain conformal field theories (NCFTs). We show that the algebraic structure of the NCFTs naturally embeds into critical lattice quantum field theory, yielding emergent topological features characteristic of gapless fermionic systems with non-zero Chern numbers. We develop a new representation of construction A of code CFT in terms of root and weight lattices of Lie algebras, focusing in particular on SU(2) and SU(3). We then derive the spectrum of particle states occupying the lattice and, with the help of fermionisation techniques, demonstrate that it hosts fermionic excitations with Dirac cones akin to tight binding systems namely the Haldane model of quantum anomalous hall effect on a honeycomb geometry.

hep-th↗

arXiv2025

Higher spin swampland conjecture for massive AdS$_{3}$ gravity

In this paper, we show that a possible version of the swampland weak gravity conjecture for higher spin (HS) massive topological AdS$_{3}$ gravity can be expressed in terms of mass $M_{hs}$, charge $Q_{hs}$ and coupling constant $g_{hs}$ of 3D gravity coupled to higher spin fields as $M_{hs} \leq \sqrt{2}$ $Q_{hs}$ $g_{hs}$ $M_{Pl}$. The higher spin charge is given by the $SO(1,2)$ quadratic Casimir $Q_{hs}^{2}=s\left (s-1\right) $ and the HS coupling constant by ${\large g}_{hs} ^{2}=2/\left (M_{Pl}^{2} l_{AdS_{3}}^{2}\right )$ while the mass expressed like $\left( l_{AdS_{3}} \text{M}_{hs}\right) ^{2}$ is defined as $ \left (1+μl_{AdS_{3}} \right ) ^{2} s \left ( s-1 \right ) +[1- \left ( μl_{AdS_{3}} \right ) ^{2} \left ( s-1 \right ) ]$.

hep-th↗

arXiv2025

Black hole solutions of three dimensional E$_{6}$-gravity

This paper aims to construct exceptional Banados-Teitelboim-Zanelli (BTZ) black holes carrying E$_{6}$ charges as solutions to the 3D higher spin Anti-de Sitter (AdS) gravity with E$_{6}$ boundary conditions. Guided by Tits-Satake graphs of real forms of the e$_{6} $ Lie algebra, we build three remarkable E$_{6}$-higher spin black hole models: the linear-exceptional and the ortho-exceptional BTZ solutions result from splitting the extremal nodes in the E$_{6\left( 6\right)}$ Tits-Satake diagram while the pure exceptional-exceptional model follows from the folding down to F$_{4\left( 4\right) }$. And with the help of Hasse diagram visualizations, we study the ensuing higher spin spectrums to develop the corresponding metrics using two types of gauge transformations. For completeness, we examine the thermodynamics of the standard BTZ coupled to E$_{6}$ higher spin gravity fields by computing the partition function exploiting a one to one correspondence between the factors of the vacuum characters and the roots of the E$_{6}$ root system.

hep-th↗

arXiv2025

Fluctuating Ensemble Averages and the BTZ Threshold

Recent work shows fascinating links between ensemble averaging and the Swampland program. In order to break the emerging global symmetries of the ensemble averaging as dictated by the no global symmetries conjecture, one may consider fluctuations away from the average given by deviations in the Siegel-Weil formula. In this work, we investigate the physical interpretation of these fluctuations in the bulk physics and pinpoint the states giving rise to them. For this purpose, we explore an ensemble of generalised Narain CFTs and build the AdS$_{3}$ gravitational dual in the Chern-Simons (CS) framework. We study the associated charged BTZ black hole solution and assess its stability. Using the Swampland weak gravity conjecture, we show that the fluctuations of the ensemble average are below the BTZ threshold and correspond to a sublattice of superextremal states emitted by the black hole. We exploit the logarithmic density of states to derive bounds on the charged vectors of the abelian CS symmetry and introduce a novel formulation of the density function to ensure consistency with the sublattice WGC. We establish bounds that allows to distinguish heavy states contributing to the average from light states generating fluctuations around it.

hep-th↗

arXiv2024

Finiteness of 3D higher spin gravity Landscape

We give Swampland constraints on the three dimensional Landscape of Anti-de Sitter higher spin gravity in the Chern-Simons formulation with connection valued in various split real forms of Lie algebras. We derive the finiteness conjecture by computing the upper bound on the rank of possible gauge groups then we refine it using the AdS distance conjecture. We discuss the implications of this Swampland constraint on the spectrum of higher spin gravity theories and we compare it with the gravitational exclusion principle required from BTZ black hole consideration to excerpt a constraint on the Chern-Simons level k.

hep-th↗

arXiv2024

Topological 4D gravity and gravitational defects

Using the Chern-Simons formulation of AdS3 gravity as well as the Costello-Witten-Yamazaki (CWY) theory for quantum integrability, we construct a novel topological 4D gravity given by Eq(5.1) with observables based on gravitational gauge field holonomies. The field action $S^{grav}_{4D}$ of this gravity has a gauge symmetry $SL(2,\mathbb{C})$ and reads also as the difference $S^{CWY_{L}}_{4D}-S^{CWY_{R}}_{4D}$ with 4D Chern-Simons field actions $S^{CWY_{L/R}}_{4D}$ given by left/right CWY theory Eq(3.9). We also use this 4D gravity derivation to build observables describing gravitational topological defects and their interactions. We conclude our study with few comments regarding quantum integrability and the extension of AdS$_{3}$/CFT$_{2}$ correspondence with regard to the obtained topological 4D gravity.

hep-th↗

arXiv2024

Black Flowers and Real Forms of Higher Spin Symmetries

Using Chern-Simons formulation, we investigate higher spin (HS) black holes in AdS$_{3}$ with soft Heisenberg hair and establish linkage with the real forms of the underlying complexified gauge symmetries taken here as $SL(N,C)_{L}\times SL(N,C)_{R}.$ We study the various conserved currents characterizing the HS black flowers (HS-BF) and show that they can be formed of layers indexed by the elements of the centre of the gauge symmetry. This feature follows from requiring the holonomy of the asymptotic gauge connection around the thermal cycle to sit in the centre $\mathbb{Z}_{N}$ of the symmetry group. With regard to the compact subgroups of the real forms of the complexified gauge symmetry, we calculate the entropies of the HS-BF and verify that, unless we are considering trivial holonomies, there are no continuous paths joining the HS-BF to the core spin 2 black holes. As explicit illustrations, we give quantum field realisations of the soft Heisenberg hair in terms of bosonic and fermionic primary conformal fields and compute the HS-BF entropy as a function of the number of fermions occupying the ground state of the Heisenberg soft hair.

hep-th↗

arXiv2024

Asymptotic Weak Gravity Conjecture in M-theory on K3 $\times$ K3

The Asymptotic WGC has been proposed as a special case of the tower WGC that probes infinite distances in the moduli space corresponding to weakly coupled gauge regimes. The conjecture has been studied in M-theory on Calabi-Yau threefold (CY3) with finite volume inducing a 5D effective QFT. In this paper, we extend the scope of the previous study to encompass lower dimensions, particularly we generalise the obtained 5D asymptotic WGC to the effective field theory $EFT_{3D}$ coupled to 3D gravity that descends from M-theory compactified on Calabi-Yau fourfold with an emphasis on K3 x K3. We find that the CY4 has three fibration structures labelled as line Type-$T^2$, surface Type-$S$ and bulk Type-$V$. The emergent $EFT_{3D}$ is shown to have 2+2 towers of states occupied by light and heavy BPS as well as non BPS particles. To ensure the viability of the 3D Asymptotic WGC, we give explicit calculations to thoroughly test the swampland constraint for both the weakly and strongly gauge coupled regimes. Additional aspects, including the gauge symmetry breaking and duality symmetry are also investigated.

hep-th↗

arXiv2023

Embedding Integrable Superspin Chain in String Theory

Using results on topological line defects of 4D Chern-Simons theory and the algebra/cycle homology correspondence in complex surfaces $\mathcal{S}$ with ADE singularities, we study the graded properties of the $sl(m|n)$ chain and its embedding in string theory. Because of the $\mathbb{Z}_{2}$-grading of $ sl(m|n)$, we show that the $\left( m+n\right) !/m!n!$ varieties of superspin chains with underlying super geometries have different cycle homologies. We investigate the algebraic and homological features of these integrable quantum chains and give a link between graded 2-cycles and genus-g Rieman surfaces $Σ_{g}$. Moreover, using homology language, we yield the brane realisation of the $sl(m|n)$ chain in type IIA string and its uplift to M-theory. Other \textrm{aspects} like graded complex surfaces with $sl(m|n)$ singularity as well as super magnons are also described.

hep-th↗

arXiv2023

't Hooft lines of ADE-type and Topological Quivers

We investigate 4D Chern-Simons theory with ADE gauge symmetries in the presence of interacting Wilson and 't Hooft line defects. We analyse the intrinsic properties of these lines' coupling and explicate the building of oscillator-type Lax matrices verifying the RLL integrability equation. We propose gauge quiver diagrams Q$_{G}^{μ}$ encoding the topological data carried by the Lax operators and give several examples where Darboux coordinates are interpreted in terms of topological bi-fundamental matter. We exploit this graphical description $\left( i\right) $ to give new results regarding solutions in representations beyond the fundamentals of $sl_{N}$, $% so_{2N}$ and $e_{6,7}$, and $\left( ii\right) $ to classify the Lax operators for simply laced symmetries in a unified E$_{7}$ CS theory. For quick access, a summary list of the leading topological quivers Q$% _{ADE}^{μ}$ is given in the conclusion section [Figures 29.(a-e), 30.(a-d) and 31.(a-d)].

hep-th↗

arXiv2023

From orthosymplectic structure to super topological matter

Topological supermatter is given by ordinary topological matter constrained by supersymmetry or graded supergroups such as OSP(2N|2N). Using results on super oscillators and lattice QFT$_{d}$, we construct a super tight binding model on hypercubic super lattice with supercharge $ \boldsymbol{Q}=\sum_{\mathbf{k}}\hat{F}_{\mathbf{k}}.\boldsymbol{q}_{\mathbf{k}}.\hat{B}_{\mathbf{k}}$. We first show that the algebraic triplet $(Ω,G,J)$ of super oscillators can be derived from the $OSp(2N|2N)$ supergroup containing the symplectic $Sp(2N)$ and the orthogonal $SO(2N)$ as even subgroups. Then, we apply the obtained result on super oscillating matter to super bands and investigate its topological obstructions protected by TPC symmetries. We also give a classification of the Bose/Fermi coupling matrix $\boldsymbol{q}_{\mathbf{k}}$ in terms of subgroups of $OSp(2N|2N)$\ and show that there are $2P_{N}$ (partition of $N$) classes $\boldsymbol{q}_{\mathbf{k}}$ given by unitary subgroups of $U\left( 2\right) \times U\left( N\right) $. Other features are also given.

hep-th↗

arXiv2022

Lax Operator and superspin chains from 4D CS gauge theory

We study the properties of interacting line defects in the four-dimensional Chern Simons (CS) gauge theory with invariance given by the $SL\left( m|n\right) $ super-group family. From this theory, we derive the oscillator realisation of the Lax operator for superspin chains with $SL(m|n)$ symmetry. To this end, we investigate the holomorphic property of the bosonic Lax operator $\mathcal{L}$ and build a differential equation $% \mathfrak{D}\mathcal{L}=0$ solved by the Costello-Gaioto-Yagi realisation of $\mathcal{L}$ in the framework of\ the CS theory. We generalize this construction to the case of gauge super-groups, and develop a Dynkin super-diagram algorithm to\ deal with the decomposition of the Lie superalgebras. We obtain the generalisation of the Lax operator describing the interaction between the electric Wilson super-lines and the magnetic 't Hooft super-defects. This coupling is given in terms of a mixture of bosonic and fermionic oscillator degrees of freedom in the phase space of magnetically charged 't Hooft super-lines. The purely fermionic realisation of the superspin chain Lax operator is also investigated and it is found to coincide exactly with the $\mathbb{Z}_{2}$- gradation of Lie superalgebras.\ \newline Keywords: 4D Chern-Simons theory, Super-gauge symmetry, Lie superalgebras and Dynkin super-diagrams, Superspin chains and integrability, Super- Lax operator.

hep-th↗

arXiv2022

A signature index for third order topological insulators

In this work, we develop an index signature characterising the third order topological phases in 3D systems. This index is an alternating sum of monomial signatures of Higgs triplet values at 3D corners. We extend our method to N-dimensional systems with open boundaries, and demonstrate that the topological invariant can be efficiently generalised to any space dimension including the second order topological insulators. Known results on lower dimensional systems are recovered and an interpretation in the Higgs space parameters is given.

cond-mat.mes-hall↗

arXiv2021

5D N=1 super QFT: symplectic quivers

We develop a method to build new 5D $\mathcal{N}=1$ gauge models based on Sasaki-Einstein manifolds $Y^{p,q}.$ These models extend the standard 5D ones having a unitary SU$\left( p\right) _{q}$ gauge symmetry based on $% Y^{p,q}$. Particular focus is put on the building of a gauge family with symplectic SP$\left( 2r,\mathbb{R}\right) $ symmetry. These super QFTs are embedded in M-theory compactified on folded toric Calabi-Yau threefolds $% \hat{X}(Y^{2r,0})$ constructed from conical $Y^{2r,0}$. By using outer-automorphism symmetries of 5D $\mathcal{N}=1$\textbf{\ }BPS quivers with unitary SU$\left( 2r\right) $ gauge invariance, we also construct BPS quivers with symplectic SP$\left( 2r,\mathbb{R}\right) $ gauge symmetry. Other related aspects are discussed. Keywords: SCFT$_{5}$, 5D $\mathcal{N}=1$ super QFT on a finite circle, Sasaki-Einstein manifolds, BPS quivers, outer-automorphisms.

hep-th↗

arXiv2020

Quantum line operators from Lax pairs

Motivated by the realisation of Yang-Baxter equation of 2d Integrable models in the 4d gauge theory of Costello-Witten-Yamazaki (CWY), we study the embedding of integrable 2d Toda field models inside this construction. This is done by using the Lax formulation of 2d integrable systems and by thinking of the standard Lax pair $L_{\pm }$ in terms of components of CWY gauge connection propagating along particular directions in the gauge bundle. We also use results of the CWY theory to build quantum line operators for 2d Toda models and compute the one loop contribution of two intersecting lines exchanging one gluon. Other features like local symmetries and comments on extension of our method to other 2d integrable models are also discussed. We also comment on\textrm{\ }some basic points that still need a refinement before talking about a fully consistent embedding of Lax pairs into CWY theory.

hep-th↗

arXiv2018

Gapped gravitinos, isospin $\frac{\mathbf{1}}{2}$ particles and $\mathcal{N}=2$ partial breaking

Using results on topological band theory of phases of matter and discrete symmetries, we study topological properties of band structure of physical systems involving spin $\frac{1}{2}$ and $\frac{3}{2}$ fermions. We apply this approach to study partial breaking in 4D $\mathcal{N}=2$ gauged supergravity in rigid limit and we describe the fermionic gapless mode in terms of chiral anomaly. We study as well the homologue of the usual spin-orbit coupling $\vec{L}.\vec{S}$, that opens the vanishing band gap for free $s=\frac{1}{2}$ fermions; and show that is precisely given by the central extension of the $\mathcal{N}=2$ supercurrent algebra in 4D spacetime. We also give comments on the rigid limit of Andrianopoli et al obtained in [28] and propose an interpretation of energy bands in terms of a chiral gapless isospin $\frac{1}{2}$-particle (iso-particle). Other features, such as discrete T- symmetry in FI coupling space, effect of quantum fluctuations and the link with Nielson-Ninomiya theorem, are also studied.

hep-th↗