arXiv subjects

Ivan Karpov

Publications and source records attributed to Ivan Karpov.

13 recordsLinked to original sources

arXiv2026

The quantum Hikita conjecture via quasimaps

We propose a refinement of the quantum Hikita conjecture of Kamnitzer, McBreen, and Proudfoot that bridges the representation theory of Coulomb branches with the enumerative geometry of Higgs branches. We also introduce a general framework for proving it, which we carry out for ADE quiver gauge theories with minuscule framings and for the gauge theory corresponding to the Jordan quiver. As an application, we use the resulting quantum Hikita isomorphisms to give a geometric description of graded traces on quantized Coulomb branches.

math.AG↗

arXiv2026

On the Feyzbakhsh-Thomas programme for Fano $3$-folds

Let $X$ be a Fano $3$-fold with even canonical class which satisfies the generalized Bogomolov-Gieseker inequality, such as $\mathbb P^3$. We express Donaldson-Thomas invariants counting Gieseker semistable sheaves of rank $r$, where $r > 0$, on $X$ in terms of those counting sheaves of rank $0$ and pure dimension $2$. This implements an analogue of the programme initiated by S. Feyzbakhsh and R. Thomas in the case of Calabi-Yau varieties. The methods include $K$-theoretic Donaldson-Thomas theory and, quite unexpectedly, the use of certain combinatorial properties of vertex algebras.

math.AG↗

arXiv2026

Rationality and symmetry of stable pairs generating series of Fano 3-folds

The generating series of descendent invariants of stable pairs on 3-folds is conjectured to be rational and to satisfy a $q\leftrightarrow q^{-1}$ symmetry. We prove this conjecture for Fano 3-folds. We utilize the same path of stability conditions that Toda used in his proof of the Calabi--Yau version of the conjecture, relating stable pairs and $L$ invariants, and work of the two authors that allows an extension of Joyce's descendent wall-crossing formula to non-standard hearts of $D^b(X)$. We use Ehrhart theory to deal with the combinatorics coming out of the wall-crossing formula. Furthermore, we specialize the wall-crossing formula to primary insertions and prove a strong rationality result predicted by the Pandharipande--Thomas/Gopakumar--Vafa correspondence.

math.AG↗

arXiv2025

Generalized K-theoretic invariants and wall-crossing via non-abelian localization

Given an abelian category and a stability condition satisfying appropriate conditions, we define generalized $K$-theoretic invariants and prove that they satisfy wall-crossing formulas. For this, we introduce a new associative algebra structure on the $K$-homology of the stack of objects of an abelian category, which we call the $K$-Hall algebra. We first define $\delta$-invariants directly coming from the stack of semistable objects and use the $K$-Hall algebra to take a formal logarithm and construct $\varepsilon$-invariants. We prove that these satisfy appropriate wall-crossing formulas using the non-abelian localization theorem. Based on work of Joyce in the cohomological setting, Liu had previously defined similar invariants assuming the existence of a framing functor; we show that when their definition of invariants makes sense it agrees with ours. Our results extend Joyce--Liu wall-crossing to non-standard hearts of $D^b(X)$, for which framing functors are not known to exist.

math.AG↗

arXiv2025

Threshold for loss of Landau damping in double-harmonic rf systems

Landau damping is a natural stabilization mechanism that mitigates coherent beam instabilities. In the longitudinal plane, loss of Landau damping (LLD) occurs when a coherent mode of oscillation emerges from the incoherent band of the bunch synchrotron frequencies. This work extends the recent LLD studies to the relevant case of double-harmonic rf systems. Specifically, it is shown that in the bunch shortening mode (both rf systems in phase at the bunch position for a non-accelerating bucket), inductive impedance above transition energy results in a vanishing LLD threshold for a binominal particle distribution, similar to the single-harmonic rf case. In this configuration, refined analytical estimates of the synchrotron frequency distribution enabled the derivation of an analytical equation for the LLD threshold by introducing an upper cutoff frequency to the impedance. The LLD threshold is studied through the concept of van Kampen modes and takes into account the effect of the voltage ratio, as well as the relative phase between the two rf systems for an inductive impedance above transition energy (or capacitive below). The validity of the theoretical studies is supported by extensive beam measurements conducted under different bucket-filling conditions in two synchrotrons, the PS and the SPS at CERN. Beyond the analytical estimates, the observations are moreover compared with the semi-analytical code MELODY and macroparticle tracking simulations in BLonD.

physics.acc-ph↗

arXiv2024

Beam-cavity interactions in the rapid cycling synchrotron chain of the future muon collider

The International Muon Collider Collaboration (IMCC) is engaged in a design study for a future facility intended to collide muons. Subsequent to the initial linear acceleration, the counter-rotating muons and anti-muons are accelerated in a chain of rapid cycling synchrotrons (RCS) up to the multi-TeV collision energy. To maximise the number of muons available in the collider, it is essential to exploit the time dilation of the muon lifetime by employing a large accelerating gradient. The 1.3 GHz TESLA cavity serves as the baseline for the RCS chain. Considering the high bunch population and the small aperture of the cavity, the resulting beam-induced voltage per bunch passage is considerable, resulting in a substantial perturbation of the cavity voltage for subsequent bunch passages. In this contribution, the effects of beam loading during the acceleration cycle on the muons are calculated with the objective of determining the optimum parameters for minimising the cavity voltage transients. The interaction of the induced voltages, considering the counter-rotating beams, is studied.

physics.acc-ph↗

arXiv2023

A geometric realization of the asymptotic affine Hecke algebra

A key tool for the study of an affine Hecke algebra $\mathcal{H}$ is provided by Springer theory of the Langlands dual group via the realization of $\mathcal{H}$ as equivariant $K$-theory of the Steinberg variety. We prove a similar geometric description for Lusztig's asymptotic affine Hecke algebra $J$ identifying it with the sum of equivariant $K$-groups of the squares of ${\mathbb C}^*$-fixed points in the Springer fibers, as conjectured by Qiu and Xi (the same result was also obtained by Oron Popp using different methods). As an application, we give a new geometric proof of Lusztig's parametrization of irreducible representations of $J$. We also reprove Braverman-Kazhdan's spectral description of $J$. As another application, we prove a description of the cocenters of $\mathcal{H}$ and $J$ conjectured by the first author with Braverman, Kazhdan and Varshavsky. The proof is based on a new algebraic description of $J$, which may be of independent interest.

math.RT↗

arXiv2023

Generalized threshold of longitudinal multi-bunch instability in synchrotrons

Beam stability is an essential requirement for particle accelerators. Longitudinal coupled-bunch instabilities (CBI) are driven by beam interaction with long-range wakefields induced in the resonant structures with narrow-band impedance. Single-bunch loss of Landau damping (LLD) is mainly determined by short-range wakefields excited at any geometry change of the beam pipe (broadband impedance) and leads to undamped bunch oscillations. Up to now, to define the threshold beam intensity or impedance, these two effects were evaluated separately. We developed an approach to numerically solve the stability problem in a more general case and derived a new analytical threshold. We have shown that LLD can modify the mechanism of multi-bunch instability and reduce the CBI threshold below the LLD threshold. This effect explains the existing observations in the CERN SPS and should be considered for future accelerators, such as HL-LHC, EIC, FCC, and others.

physics.acc-ph↗

arXiv2023

Transfer matrices of rational spin chains via novel BGG-type resolutions

We obtain BGG-type formulas for transfer matrices of irreducible finite-dimensional representations of the classical Lie algebras $\mathfrak{g}$, whose highest weight is a multiple of a fundamental one and which can be lifted to the representations over the Yangian $Y(\mathfrak{g})$. These transfer matrices are expressed in terms of transfer matrices of certain infinite-dimensional highest weight representations (such as parabolic Verma modules and their generalizations) in the auxiliary space. We further factorise the corresponding infinite-dimensional transfer matrices into the products of two Baxter $Q$-operators, arising from our previous study (arXiv:2001.04929, arXiv:2104.14518) of the degenerate Lax matrices. Our approach is crucially based on the new BGG-type resolutions of the finite-dimensional $\mathfrak{g}$-modules, which naturally arise geometrically as the restricted duals of the Cousin complexes of relative local cohomology groups of ample line bundles on the partial flag variety $G/P$ stratified by $B_{-}$-orbits.

math.RT↗

arXiv2022

Beam Longitudinal Dynamics Simulation Suite BLonD

The beam longitudinal dynamics code BLonD has been developed at CERN since 2014 and has become a central tool for longitudinal beam dynamics simulations. In this paper, we present this modular simulation suite and the various physics models that can be included and combined by the user. We detail the reference frame, the equations of motion, the BLonD-specific options for radio-frequency parameters such as phase noise, fixed-field acceleration, and feedback models for the CERN accelerators, as well as the modeling of collective effects and synchrotron radiation. We also present various methods of generating multi-bunch distributions matched to a given impedance model. BLonD is furthermore a well-tested and optimized simulation suite, which is demonstrated through examples, too.

physics.acc-ph↗

arXiv2022

Longitudinal mode-coupling instabilities of proton bunches in the CERN Super Proton Synchrotron

In this paper, we study single-bunch instabilities observed in the CERN Super Proton Synchrotron (SPS). According to the linearized Vlasov theory, radial or azimuthal mode-coupling instabilities result from a coupling of bunch-oscillation modes, which belong to either the same or adjacent azimuthal modes, respectively. We show that both instability mechanisms exist in the SPS by applying the Oide-Yokoya approach to compute van Kampen modes for the realistic longitudinal impedance model of the SPS. The results agree with macroparticle simulations and are consistent with beam measurements. In particular, we see that the uncontrolled longitudinal emittance blow-up of single bunches observed before the recent impedance reduction campaign (2018-2021) is due to the radial mode-coupling instability. Unexpectedly, this instability is as strong as the azimuthal mode-coupling instability, which is possible in the SPS for other combinations of bunch length and intensity. We also demonstrate the significant role of rf nonlinearity and potential-well distortion in determining these instability thresholds. Finally, we discuss the effect of the recent impedance reduction campaign on beam stability in single- and double-rf configurations.

physics.acc-ph↗

arXiv2022

Muon Collider Physics Summary

The perspective of designing muon colliders with high energy and luminosity, which is being investigated by the International Muon Collider Collaboration, has triggered a growing interest in their physics reach. We present a concise summary of the muon colliders potential to explore new physics, leveraging on the unique possibility of combining high available energy with very precise measurements.

hep-ph↗

arXiv2020

Thresholds for loss of Landau damping in longitudinal plane

Landau damping mechanism plays a crucial role in providing single-bunch stability in LHC, High-Luminosity LHC, other existing as well as previous and future (like FCC) circular hadron accelerators. In this paper, the thresholds for the loss of Landau damping (LLD) in the longitudinal plane are derived analytically using the Lebedev matrix equation (1968) and the concept of the emerged van Kampen modes (1983). We have found that for the commonly-used particle distribution functions from a binomial family, the LLD threshold vanishes in the presence of the constant inductive impedance Im$Z/k$ above transition energy. Thus, the effect of the cutoff frequency or the resonant frequency of a broad-band impedance on beam dynamics is studied in detail. The findings are confirmed by direct numerical solutions of the Lebedev equation as well as using the Oide-Yokoya method (1990). Moreover, the characteristics, which are important for beam operation, as the amplitude of residual oscillations and the damping time after a kick (or injection errors) are considered both above and below the threshold. Dependence of the threshold on particle distribution in the longitudinal phase space is also analyzed, including some special cases with a non-zero threshold for Im$Z/k = const$. All main results are confirmed by macro-particle simulations and consistent with available beam measurements in the LHC.

physics.acc-ph↗