arXiv subjects

Ori J. Ganor

Publications and source records attributed to Ori J. Ganor.

At least 19 recordsLinked to original sources

arXiv2026

Analysis of Quartic Potential Problems Using Fredholm Integral Operators with Airy Functions

Fredholm integral operators that commute with the Hamiltonians of certain quantum mechanical systems with quartic potentials are introduced in closed analytical form. The operators are expressed in terms of the Airy function, and their eigenvalues fall off exponentially. Using these operators we obtain an exact dual description in terms of infinite one-dimensional chains. The systems discussed include the anharmonic quartic oscillator as well as multivariable potentials and higher dimensional systems. We compute a few moments of the Fredholm operators, using matrix models in the higher dimensional case, and we show how those can be used to approximate the energy spectrum and obtain estimates of the asymptotic behavior of the wavefunctions.

hep-th↗

arXiv2024

Ground States of Class S Theory on ADE Singularities and dual Chern-Simons theory

In radial quantization, the ground states of a gauge theory on ADE singularities $\mathbb{R}^4/Γ$ are characterized by flat connections that are maps from $Γ$ to the gauge group. We study Class $\mathcal{S}$ theory of type $\mathfrak{a}_1=\mathfrak{su}(2)$ on a Riemann surface of genus $g>1$, without punctures. The fundamental building block of Class $\mathcal{S}$ theory is the trifundamental Trinion theory - a low energy limit of two M5 branes compactified on the three-punctured Riemann sphere. We show, through the superconformal index, that the supersymmetric Casimir energy of the trifundamental theory imposes a constraint on the set of allowed flat connections, which agrees with the prediction of a duality relating the ground state Hilbert space of Class $\mathcal{S}$ on ADE singularities to the Hilbert space of a certain dual Chern-Simons theory whose gauge group is given by the McKay correspondence. The conjecture is shown to hold for $Γ=\mathbb{Z}_k$, agreeing with the previous results of Benini et al. and Alday et al. A non-abelian generalization of this duality is analyzed by considering the example of the dicyclic group $Γ=\text{Dic}_2$, corresponding to Chern-Simons gauge group SO$(8)$.

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arXiv2024

Timelike Kasner singularities and Floquet States in 2+1d AdS/CFT

We consider a model of a holographic 2+1d CFT interacting with an oscillating background gauge field. It is solved by an AdS-Vaidya metric describing Ohmic heating of the boundary field theory. However, we also show that if timelike singularities of Kasner type are permitted then a time independent solution that may be interpreted as a Floquet state of the system can be constructed. In this state the system exhibits either Hall conductivity or kinetic induction, and we numerically evaluate the Kasner exponents for a range of boundary conditions. This model may contribute to the ongoing discussion on the validity and meaning of the Kasner metric in the AdS/CFT correspondence and its application in cosmology.

hep-th↗

arXiv2022

On Pidduck polynomials and zeros of the Riemann zeta function

For $1<p<\infty$, we prove that a necessary and sufficient condition for $s$ to be a zero of the Riemann zeta function in the strip $0<\Re s<1$ is that $$\left(\begin{array}{cccccc} 1 & \frac{1}{3} & \frac{1}{5} & \frac{1}{7} & \frac{1}{9} & \cdots \\ -\frac{s}{3} & 1 & \frac{1}{3} & \frac{1}{5} & \frac{1}{7} & \cdots \\ -\frac{s}{5} & -\frac{s}{5} & 1 & \frac{1}{3} & \frac{1}{5} & \cdots \\ -\frac{s}{7} &-\frac{s}{7} & -\frac{s}{7} & 1 & \frac{1}{3} & \cdots \\ -\frac{s}{9} & -\frac{s}{9} & -\frac{s}{9} & -\frac{s}{9} & 1 & \cdots \\ \vdots &\vdots & \vdots &\vdots & \vdots & \ddots\\ \end{array}\right)\left(\begin{array}{c} v_0 \\ v_1 \\ v_2 \\ v_3 \\ v_4 \\ \vdots \\ \vdots \\ \end{array}\right) =0 $$ has a nontrivial solution $\left(v_{k}\right)_{k=0}^\infty$ in $\ell^p$. A similar matrix equation was discovered by K. M. Ball in 2017, but the current paper offers a different (and independent) perspective. In this paper an explicit formula for $v_{k}$ is constructed in terms of Pidduck polynomials. In the process, it is also shown that Pidduck polynomials form an orthogonal basis with respect to an inner product of polynomials $f,g$ whereby we replace in a formal expression "$\sum_{n=1}^\infty (-1)^{n+1}n \overline{f(n^2)} g(n^2)$" the divergent sums "$\sum_{n=1}^\infty (-1)^{n+1}n^{1+2k}$" with their zeta-function regularized values. We also discuss the modification for possible non-simple zeros and conclude with applications to the question of the simplicity of the zeros and a relation to the Hilbert-Pólya program.

math.NT↗

arXiv2020

Double-Janus Linear Sigma Models and Generalized Reciprocity for Gauss Sums

We study the supersymmetric partition function of a 2d linear $σ$-model whose target space is a torus with a complex structure that varies along one worldsheet direction and a Kähler modulus that varies along the other. This setup is inspired by the dimensional reduction of a Janus configuration of 4d $\mathcal{N}=4$ $U(1)$ Super-Yang-Mills theory compactified on a mapping torus ($T^2$ fibered over $S^1$) times a circle with an $SL(2,\mathbb{Z})$ duality wall inserted on $S^1$, but our setup has minimal supersymmetry. The partition function depends on two independent elements of $SL(2,\mathbb{Z})$, one describing the duality twist, and the other describing the geometry of the mapping torus. It is topological and can be written as a multivariate quadratic Gauss sum. By calculating the partition function in two different ways, we obtain identities relating different quadratic Gauss sums, generalizing the {\it Landsberg-Schaar} relation. These identities are a subset of a collection of identities discovered by F. Deloup. Each identity contains a phase which is an eighth root of unity, and we show how it arises as a Berry phase in the supersymmetric Janus-like configuration. Supersymmetry requires the complex structure to vary along a semicircle in the upper half-plane, as shown by Gaiotto and Witten in a related context, and that semicircle plays an important role in reproducing the correct Berry phase.

hep-th↗

arXiv2017

Supersymmetric interactions of a six-dimensional self-dual tensor and fixed-shape second quantized strings

"Curvepole (2,0)-theory" is a deformation of the (2,0)-theory with nonlocal interactions. A "curvepole" is defined as a two-dimensional generalization of a dipole. It is an object of fixed two-dimensional shape whose boundary is a charged curve that interacts with a two-form gauge field. Curvepole theory was previously only defined indirectly via M-theory. Here we propose a supersymmetric Lagrangian, constructed explicitly up to quartic terms, for an "abelian" curvepole theory, which is an interacting deformation of the free (2,0) tensor mutliplet. This theory contains fields whose quanta are curvepoles (i.e., fixed-shape strings). Supersymmetry is preserved (at least up to quartic terms) if the shape of the curvepoles is (2d) planar. This nonlocal 6d QFT may also serve as a UV completion for certain (local) 5d gauge theories.

hep-th↗

arXiv2015

Q-balls of Quasi-particles in a (2,0)-theory model of the Fractional Quantum Hall Effect

A toy model of the fractional quantum Hall effect appears as part of the low-energy description of the Coulomb branch of the $A_1$ (2,0)-theory formulated on $(S^1\times R^2)/Z_k$, where the generator of $Z_k$ acts as a combination of translation on $S^1$ and rotation by $2π/k$ on $R^2$. At low energy the configuration is described in terms of a 4+1D Super-Yang-Mills theory on a cone ($R^2/Z_k$) with additional 2+1D degrees of freedom at the tip of the cone that include fractionally charged particles. These fractionally charged quasi-particles are BPS strings of the (2,0)-theory wrapped on short cycles. We analyze the large $k$ limit, where a smooth cigar-geometry provides an alternative description. In this framework a W-boson can be modeled as a bound state of $k$ quasi-particles. The W-boson becomes a Q-ball, and it can be described as a soliton solution of Bogomolnyi monopole equations on a certain auxiliary curved space. We show that axisymmetric solutions of these equations correspond to singular maps from $AdS_3$ to $AdS_2$, and we present some numerical results and an asymptotic expansion.

hep-th↗

arXiv2014

Janus configurations with SL(2,Z)-duality twists, Strings on Mapping Tori, and a Tridiagonal Determinant Formula

We develop an equivalence between two Hilbert spaces: (i) the space of states of $U(1)^n$ Chern-Simons theory with a certain class of tridiagonal matrices of coupling constants (with corners) on $T^2$; and (ii) the space of ground states of strings on an associated mapping torus with $T^2$ fiber. The equivalence is deduced by studying the space of ground states of $SL(2,Z)$-twisted circle compactifications of $U(1)$ gauge theory, connected with a Janus configuration, and further compactified on $T^2$. The equality of dimensions of the two Hilbert spaces (i) and (ii) is equivalent to a known identity on determinants of tridiagonal matrices with corners. The equivalence of operator algebras acting on the two Hilbert spaces follows from a relation between the Smith normal form of the Chern-Simons coupling constant matrix and the isometry group of the mapping torus, as well as the torsion part of its first homology group.

hep-th↗

arXiv2012

Ground States of Duality-twisted Sigma-Models with K3 Target Space

We analyze the ground states of a two-dimensional sigma-model whose target space is an elliptically fibered K3, with the sigma-model compactified on a circle with boundary conditions twisted by a duality symmetry. We show that the Witten index receives contributions from two kinds of states: (i) those that can be mapped to cohomology with coefficients in a certain line bundle over the target space, and (ii) states whose wave-functions are localized at singular fibers. We also discuss the orbifold limit and possible connections with geometric quantization of the target space.

hep-th↗

arXiv2012

Static Charges in the Low-Energy Theory of the S-Duality Twist

We continue the study of the low-energy limit of N=4 super Yang-Mills theory compactified on a circle with S-duality and R-symmetry twists that preserve N=6 supersymmetry in 2+1D. We introduce external static supersymmetric quark and anti-quark sources into the theory and calculate the Witten Index of the resulting Hilbert space of ground states on a torus. Using these results we compute the action of simple Wilson loops on the Hilbert space of ground states without sources. In some cases we find disagreement between our results for the Wilson loop eigenvalues and previous conjectures about a connection with Chern-Simons theory.

hep-th↗

arXiv2010

Ground States of S-duality Twisted N=4 Super Yang-Mills Theory

We study the low-energy limit of a compactification of N=4 U(n) super Yang-Mills theory on $S^1$ with boundary conditions modified by an S-duality and R-symmetry twist. This theory has N=6 supersymmetry in 2+1D. We analyze the $T^2$ compactification of this 2+1D theory by identifying a dual weakly coupled type-IIA background. The Hilbert space of normalizable ground states is finite-dimensional and appears to exhibit a rich structure of sectors. We identify most of them with Hilbert spaces of Chern-Simons theory (with appropriate gauge groups and levels). We also discuss a realization of a related twisted compactification in terms of the (2,0)-theory, where the recent solution by Gaiotto and Witten of the boundary conditions describing D3-branes ending on a (p,q) 5-brane plays a crucial role.

hep-th↗

arXiv2008

Selfduality and Chern-Simons Theory

We propose a relation between the operator of S-duality (of N=4 super Yang-Mills theory in 3+1D) and a topological theory in one dimension lower. We construct the topological theory by compactifying N=4 super Yang-Mills on a circle with an S-duality and R-symmetry twist. The S-duality twist requires a selfdual coupling constant. We argue that for a sufficiently low rank of the gauge group the three-dimensional low-energy description is a topological theory, which we conjecture to be a pure Chern-Simons theory. This conjecture implies a connection between the action of mirror symmetry on the sigma-model with Hitchin's moduli space as target space and geometric quantization of the moduli space of flat connections on a Riemann surface.

hep-th↗

arXiv2007

A New Lorentz Violating Nonlocal Field Theory From String-Theory

A four-dimensional field theory with a qualitatively new type of nonlocality is constructed from a setting where Kaluza-Klein particles probe toroidally compactified string theory with twisted boundary conditions. In this theory fundamental particles are not pointlike and occupy a volume proportional to their R-charge. The theory breaks Lorentz invariance but appears to preserve spatial rotations. At low energies, it is approximately N=4 Super Yang-Mills theory, deformed by an operator of dimension seven. The dispersion relation of massless modes in vacuum is unchanged, but under certain conditions in this theory, particles can travel at superluminal velocities.

hep-th↗

arXiv2007

Aspects of Puff Field Theory

We describe some features of the recently constructed "Puff Field Theory," and present arguments in favor of it being a field theory decoupled from gravity. We construct its supergravity dual and calculate the entropy of this theory in the limit of large 't Hooft coupling. We also determine the leading irrelevant operator that governs its deviation from N=4 super Yang-Mills theory.

hep-th↗

arXiv2005

A Deformation of Twistor Space and a Chiral Mass Term in N=4 Super Yang-Mills Theory

Super twistor space admits a certain (super) complex structure deformation that preserves the Poincare subgroup of the symmetry group PSL(4|4) and depends on 10 parameters. In a previous paper [hep-th/0502076], it was proposed that in twistor string theory this deformation corresponds to augmenting N=4 super Yang-Mills theory by a mass term for the left-chirality spinors. In this paper we analyze this proposal in more detail. We calculate 4-particle scattering amplitudes of fermions, gluons and scalars and show that they are supported on holomorphic curves in the deformed twistor space.

hep-th↗

arXiv2005

E10 Orbifolds

We study Z2 orbifolds of M-theory in terms of E10. We find a simple relation between the Z2 action on E10 and the imaginary root that corresponds [hep-th/0401053] to the "twisted sector" branes. We discuss the connection between the Kac-Moody algebra DE10 and the "untwisted" sector, and we demonstrate how DE18 can describe both the untwisted and twisted sectors simultaneously.

hep-th↗

arXiv2005

Massless and Massive Three Dimensional Super Yang-Mills Theory and Mini-Twistor String Theory

We propose various ways of adding mass terms to three-dimensional twistor string theory. We begin with a review of mini-twistor space--the reduction of D=4 twistor space to D=3. We adapt the two proposals for twistor string theory, Witten's and Berkovits's, to D=3 super Yang-Mills theory. In Berkovits's model, we identify the enhanced R-symmetry. We then construct B-model topological string theories that, we propose, correspond to D=3 Yang-Mills theory with massive spinors and massive and massless scalars in the adjoint representation of the gauge group. We also analyze the counterparts of these constructions in Berkovits's model. Some of our constructions can be lifted to D=4, where infinitesimal mass terms correspond to VEVs of certain superconformal gravity fields.

hep-th↗

arXiv2004

M-theory and E10: Billiards, Branes, and Imaginary Roots

Eleven dimensional supergravity compactified on $T^{10}$ admits classical solutions describing what is known as billiard cosmology - a dynamics expressible as an abstract (billiard) ball moving in the 10-dimensional root space of the infinite dimensional Lie algebra E10, occasionally bouncing off walls in that space. Unlike finite dimensional Lie algebras, E10 has negative and zero norm roots, in addition to the positive norm roots. The walls above are related to physical fluxes that, in turn, are related to positive norm roots (called real roots) of E10. We propose that zero and negative norm roots, called imaginary roots, are related to physical branes. Adding `matter' to the billiard cosmology corresponds to adding potential terms associated to imaginary roots. The, as yet, mysterious relation between E10 and M-theory on $T^{10}$ can now be expanded as follows: real roots correspond to fluxes or instantons, and imaginary roots correspond to particles and branes (in the cases we checked). Interactions between fluxes and branes and between branes and branes are classified according to the inner product of the corresponding roots (again in the cases we checked). We conclude with a discussion of an effective Hamiltonian description that captures some features of M-theory on $T^{10}.$

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