arXiv subjects

Rubik Poghossian

Publications and source records attributed to Rubik Poghossian.

At least 19 recordsLinked to original sources

arXiv2025

On 5-point conformal block with level 2 degenerate field insertion and its AGT dual

In this paper, we develop and explore recursive methods to investigate the 2d CFT 5-point conformal block with a level 2 degenerate insertion, as well as its AGT dual, by solving the BPZ differential equation. First, we represent the solution of the differential equation as a double series expansion. On the 2-node quiver gauge theory side, this corresponds to the instanton series. We then demonstrate that the expansion coefficients are uniquely determined by a recursion relation. Inspired by the approach initiated in a paper by D. Gaiotto and J. Teschner, we partially resum this series and show that the result can be elegantly expressed in terms of a single hypergeometric function and its derivative. This new representation makes it straightforward to relate different asymptotic regions. As a by-product, this provides us a simple derivation of fusion and braiding coefficients. We describe the subtle procedure of merging the degenerate field with the outgoing state, thereby obtaining a generic 4-point block, which on the gauge theory side corresponds to the partition function of $SU(2)$ gauge theory with four massive hypermultiplets in the $Ω$-background. Finally, we performed several nontrivial checks that confirm our results.

hep-th↗

arXiv2025

Resumming Post-Minkowskian and Post-Newtonian gravitational waveform expansions

We derive formulae that resum, at a given order in the soft limit, the infinite series of Post-Minkowskian (small gravitational coupling) or Post-Newtonian (small velocities) corrections to the gravitational waveform produced by particles moving along a general (open or closed) trajectory in the Schwarzschild geometry in the probe limit. Specifying to the case of circular orbits, we compute the waveform and the energy flux to order 30PN, and compare it against the available results in the literature. Our results are based on a novel hypergeometric representation of the solutions of the Heun equation (and its confluence), that leads to a simple mathematical proof of the Heun connection formula.

gr-qc↗

arXiv2025

A note on rank 5/2 Liouville irregular block, Painlevé 1 and the ${\cal H}_0$ Argyres-Douglas theory

We study 4d type ${\cal H}_0$ Argyres-Douglas theory in $Ω$-background by constructing Liouville irregular state of rank 5/2. The results are compared with generalized Holomorphic anomaly approach, which provides order by order expansion in $Ω$-background parameters $ε_{1,2}$. Another crucial test of our results provides comparison with respect to Painlevé 1 $τ$-function, which was expected to be hold in self-dual case $ε_1=-ε_2$. We also discuss Nekrasov-Shatashvili limit $ε_1=0$, accessible either by means of deformed Seiberg-Witten curve, or WKB methods.

hep-th↗

arXiv2025

Exact expressions for the 5-Point Liouville conformal block with a level-two degenerate field insertion

In this paper we investigate 5-point Liouville conformal block with a level 2 degenerate field insertion. Our main tool is the BPZ differential equation, which, upon placing three of the insertions at the standard positions $\infty$, $1$, and $0$, reduces to a linear differential equation which is of order two in the degenerate insertion point $z$, and order one in the remaining point $x$. In a previous paper, it was conjectured that the solution could be expressed in terms of a single hypergeometric function and its derivative, with coefficients computable via recursive relations up to the desired order $x^k$. In this paper, we simplify these recursion relations and provide a rigorous inductive proof of the conjecture. Our representation of the 5-point conformal block readily facilitates the connection between various analyticity regions through classical connection formulae for the hypergeometric function. In the quasi-classical limit, the 5-point BPZ equation reduces to the Heun equation. Consequently, we recover a recently proposed representation of the Heun equation in terms of a single hypergeometric function, which has proven to be highly effective in the analysis of gravitational perturbation of black holes.

hep-th↗

arXiv2025

A note on rank $\frac{3}{2}$ Liouville irregular block

This paper focuses on a conformal block with rank $\frac{3}{2}$ irregular singularity which corresponds to the prepotential of the ${\cal H}_1$ Argyres-Douglas theory in $Ω$ background. We derive this irregular conformal block using generalized holomorphic anomaly recursion relation. This results is an expression which is a power series in $Ω$-background parameters $ε_{1,2}$ and exact in coupling. We have verified that in small coupling regime our result is consistent with previously known expressions. Furthermore we derive the Deformed Seiberg-Witten curve which provides an alternative tool to explore above mentioned theory in Nekrasov-Shatashvili limit of $Ω$-background. We checked that the results are in complete agreement with the holomorphic anomaly approach.

hep-th↗

arXiv2023

On irregular states and Argyres-Douglas theories

Conformal theories of the Argyres-Douglas type are notoriously hard to study given that they are isolated and strongly coupled thus lacking a lagrangian description. In flat space, an exact description is provided by the Seiberg-Witten theory. Turning on a $Ω$-background makes the geometry ``quantum" and tractable only in the weak curvature limit. In this paper we use the AGT correspondence to derive $Ω$-exact formulae for the partition function, in the nearby of monopole points where the dynamics is described by irregular conformal blocks of the CFT. The results are checked against those obtained by the recursion relations coming from a conformal anomaly in the region where the two approaches overlap. The Nekrasov-Shatashvili limit is also discussed. Finally, we comment on the existence of black holes in De Sitter space whose low energy dynamics is described by an Argyres-Douglas theory.

hep-th↗

arXiv2022

CFT description of BH's and ECO's: QNMs, superradiance, echoes and tidal responses

Using conformal field theory and localization tecniques we study the propagation of waves in gravity backgrounds described by Schrödinger like equations with Fuchsian singularities. Exact formulae for the connection matrices relating the asymptotic behaviour of the wave functions near the singularities are obtained in terms of braiding and fusion rules of the CFT. The results are applied to the study of quasi normal modes, absorption cross sections, amplification factors, echoes and tidal responses of black holes (BH) and exotic compact objects (ECO) in four and five dimensions. In particular, we propose a definition of dynamical Love numbers in gravity.

hep-th↗

arXiv2022

RG flow between $W_3$ minimal models by perturbation and domain wall approaches

We explore the RG flow between neighboring minimal CFT models with $W_3$ symmetry. After computing several classes of OPE structure constants we were able to find the matrices of anomalous dimensions for three classes of RG invariant sets of local fields. Each set from the first class consists of a single primary field, the second one of three primaries, while sets in the third class contain six primary and four secondary fields. We diagonalize their matrices of anomalous dimensions and establish the explicit maps between UV and IR fields (mixing coefficients). While investigating the three point functions of secondary fields we have encountered an interesting phenomenon, namely violation of holomorphic anti-holomorphic factorization property, something that does not happen in ordinary minimal models with Virasoro symmetry solely. Furthermore, the perturbation under consideration preserves a non-trivial subgroup of $W$ transformations. We have derived the corresponding conserved current explicitly. We used this current to define a notion of anomalous $W$-weights in perturbed theory: the analog for matrix of anomalous dimensions. For RG invariant sets with primary fields only we have derived a formula for this quantity in terms of structure constants. This allowed us to compute anomalous $W$-weights for the first and second classes explicitly. The same RG flow we investigate also with the domain wall approach for the second RG invariant class and find complete agreement with the perturbative approach.

hep-th↗

arXiv2021

A Young diagram expansion of the hexagonal Wilson loop (amplitude) in ${\cal N}=4$ SYM

We shall interpret the null hexagonal Wilson loop (or, equivalently, six gluon scattering amplitude) in 4D ${\cal N}=4$ Super Yang-Mills, or, precisely, an integral representation of its matrix part, via an ADHM-like instanton construction. In this way, we can apply localisation techniques to obtain combinatorial expressions in terms of Young diagrams. Then, we use our general formula to obtain explicit expressions in several explicit cases. In particular, we discuss those already available in the literature and find exact agreement. Moreover, we are capable to determine explicitly the denominator (poles) of the matrix part, and find some interesting recursion properties for the residues, as well.

hep-th↗

arXiv2019

$T$, $Q$ and periods in $SU(3)$ ${\cal N}=2$ SYM

We consider the third order differential equation derived from the deformed Seiberg-Witten differential for pure ${\cal N}=2$ SYM with gauge group $SU(3)$ in Nekrasov-Shatashvili limit of $Ω$-background. We show that this is the same differential equation that emerges in the context of Ordinary Differential Equation/Integrable Models (ODI/IM) correspondence for $2d$ $A_2$ Toda CFT with central charge $c=98$. We derive the corresponding $QQ$ and related $TQ$ functional relations and establish the asymptotic behaviour of $Q$ and $T$ functions at small instanton parameter $q \rightarrow 0$. Moreover, numerical integration of the Floquet monodromy matrix of the differential equation leads to evaluation of the $A$-cycles $a_{1,2,3}$ at any point of the moduli space of vacua parametrised by the vector multiplet scalar VEVs $\langle \textbf{tr}\,ϕ^2\rangle$ and $\langle \textbf{tr}\,ϕ^3\rangle$ even for large values of $q$ which are well beyond the reach of instanton calculus. The numerical results at small $q$ are in excellent agreement with instanton calculation. We conjecture a very simple relation between Baxter's $T$-function and $A$-cycle periods $a_{1,2,3}$, which is an extension of Alexei Zamolodchikov's conjecture about Mathieu equation.

hep-th↗

arXiv2019

Correlation Functions of Classical and Quantum Artin System defined on Lobachevsky Plane and Scrambling Time

We consider the quantisation of the Artin dynamical system defined on the fundamental region of the modular group. In classical regime the geodesic flow in the fundamental region represents one of the most chaotic dynamical systems, it has mixing of all orders, Lebesgue spectrum and non-zero Kolmogorov entropy. As a result, the classical correlation functions decay exponentially. In order to investigate the influence of the classical chaotic behaviour on the quantum-mechanical properties of the Artin system we calculated the corresponding thermal quantum-mechanical correlation functions. It was conjectured by Maldacena, Shenker and Stanford that the classical chaos can be diagnosed in thermal quantum systems by using an out-of-time-order correlation function as well as the square of the commutator of operators separated in time. We demonstrated that the two- and four-point correlation functions of the Louiville-like operators decay exponentially with a temperature dependent exponent. As conjectured the square of the commutator of the Louiville-like operators separated in time grows exponentially, similar to the exponential divergency of trajectories in the classical regime. The corresponding exponent does not saturate the maximal growth condition.

hep-th↗

arXiv2019

Cubic Interaction for Higher Spins in $AdS_{d+1}$ space in the explicit covariant form

We present a slightly modified prescription of the radial pullback formalism proposed previously by R. Manvelyan, R. Mkrtchyan and W. Rühl in 2012, where authors investigated possibility to connect the main term of higher spin interaction in flat $d+2$ dimensional space to the main term of interaction in $AdS_{d+1}$ space ignoring all trace and divergent terms but expressed directly through the $AdS$ covariant derivatives and including some curvature corrections. In this paper we succeeded to solve all necessary \emph{recurrence relations} to finalize full radial pullback of the main term of cubic self-interaction for higher spin gauge fields in Fronsdal's formulation from flat to one dimension less $AdS_{d+1}$ space. Nontrivial solutions of recurrence relations lead to the possibility to obtain the full set of $AdS_{d+1}$ dimensional interacting terms with all curvature corrections including trace and divergence terms from any interaction term in $d+2$ dimensional flat space.

hep-th↗

arXiv2017

Recurrence relations for the ${\cal W}_3$ conformal blocks and ${\cal N}=2$ SYM partition functions

Recursion relations for the sphere $4$-point and torus $1$-point ${\cal W}_3$ conformal blocks, generalizing Alexei Zamolodchikov's famous relation for the Virasoro conformal blocks are proposed. One of these relations is valid for any 4-point conformal block with two arbitrary and two special primaries with charge parameters proportional to the highest weight of the fundamental irrep of $SU(3)$. The other relation is designed for the torus conformal block with a special (in above mentioned sense) primary field insertion. AGT relation maps the sphere conformal block and the torus block to the instanton partition functions of the ${\cal N}=2$ $SU(3)$ SYM theory with 6 fundamental or an adjoint hypermultiplets respectively. AGT duality played a central role in establishing these recurrence relations, whose gauge theory counterparts are novel relations for the $SU(3)$ partition functions with $N_f=6$ fundamental or an adjoint hypermultiplets. By decoupling some (or all) hypermultiplets, recurrence relations for the asymptotically free theories with $0\le N_f<6$ are found.

hep-th↗

arXiv2016

Deformed SW curve and the null vector decoupling equation in Toda field theory

It is shown that the deformed Seiberg-Witten curve equation after Fourier transform is mapped into a differential equation for the AGT dual 2d CFT cnformal block containing an extra completely degenerate field. We carefully match parameters in two sides of duality thus providing not only a simple independent prove of the AGT correspondence in Nekrasov-Shatashvili limit, but also an extension of AGT to the case when a secondary field is included in the CFT conformal block. Implications of our results in the study of monodromy problems for a large class of $n$'th order Fuchsian differential equations are discussed.

hep-th↗

arXiv2016

Wilson Loops and Chiral Correlators on Squashed Spheres

After a very brief recollection of how my scientific collaboration with Ugo started, in this talk I will present some recent results obtained with localization: the deformed gauge theory partition function $Z(\vecτ|q)$ and the expectation value of circular Wilson loops $W$ on a squashed four-sphere will be computed. The partition function is deformed by turning on $τ_J \,{\rm tr} \, Φ^J$ interactions with $Φ$ the ${\cal N}=2$ superfield. For the ${\cal N}=4$ theory SUSY gauge theory exact formulae for $Z$ and $W$ in terms of an underlying $U(N)$ interacting matrix model can be derived thus replacing the free Gaussian model describing the undeformed ${\cal N}=4$ theory. These results will be then compared with those obtained with the dual CFT according to the AGT correspondence. The interactions introduced previously are in fact related to the insertions of commuting integrals of motion in the four-point CFT correlator and the chiral correlators are expressed as $τ$-derivatives of the gauge theory partition function on a finite $Ω$-background.

hep-th↗

arXiv2016

The light asymptotic limit of conformal blocks in Toda field theory

We compute the light asymptotic limit of $A_{n-1}$ Toda conformal blocks by using the AGT correspondence. We show that for certain class of CFT blocks the corresponding Nekrasov partition functions in this limit are simplified drastically being represented as a sum of a restricted class of Young diagrams. In the particular case of $A_{2}$ Toda we also compute the corresponding conformal blocks using conventional CFT techniques finding a perfect agreement with the results obtained from the Nekrasov partition functions.

hep-th↗

arXiv2016

VEV of Baxter's Q-operator in N=2 gauge theory and the BPZ differential equation

In this short notes using AGT correspondence we express simplest fully degenerate primary fields of Toda field theory in terms an analogue of Baxter's $Q$-operator naturally emerging in ${\cal N}=2$ gauge theory side. This quantity can be considered as a generating function of simple trace chiral operators constructed from the scalars of the ${\cal N}=2$ vector multiplets. In the special case of Liouville theory, exploring the second order differential equation satisfied by conformal blocks including a degenerate at the second level primary field (BPZ equation) we derive a mixed difference-differential relation for $Q$-operator. Thus we generalize the $T$-$Q$ difference equation known in Nekrasov-Shatashvili limit of the $Ω$-background to the generic case.

hep-th↗

arXiv2014

Two Dimensional Renormalization Group Flows in Next to Leading Order

Zamolodchikov's famous analysis of the RG trajectory connecting successive minimal CFT models $M_p$ and $M_{p-1}$ for $p\gg 1$, is improved by including second order in coupling constant corrections. This allows to compute IR quantities with next to leading order accuracy of the $1/p$ expansion. We compute in particular, the beta function and the anomalous dimensions for certain classes of fields. As a result we are able to identify with a greater accuracy the IR limit of these fields with certain linear combination of the IR theory $M_{p-1}$. We discuss the relation of these results with Gaotto's recent RG domain wall proposal.

hep-th↗