arXiv subjects

Tin Sulejmanpasic

Publications and source records attributed to Tin Sulejmanpasic.

45 records · Page 3Linked to original sources

arXiv2015

Toward Picard-Lefschetz Theory of Path Integrals, Complex Saddles and Resurgence

We show that the semi-classical analysis of generic Euclidean path integrals necessarily requires complexification of the action and measure, and consideration of complex saddle solutions. We demonstrate that complex saddle points have a natural interpretation in terms of the Picard-Lefschetz theory. Motivated in part by the semi-classical expansion of QCD with adjoint matter on ${\mathbb R}^3\times S^1$, we study quantum-mechanical systems with bosonic and fermionic (Grassmann) degrees of freedom with harmonic degenerate minima, as well as (related) purely bosonic systems with harmonic non-degenerate minima. We find exact finite action non-BPS bounce and bion solutions to the holomorphic Newton equations. We find not only real solutions, but also complex solution with non-trivial monodromy, and finally complex multi-valued and singular solutions. Complex bions are necessary for obtaining the correct non-perturbative structure of these models. In the supersymmetric limit the complex solutions govern the ground state properties, and their contribution to the semiclassical expansion is necessary to obtain consistency with the supersymmetry algebra. The multi-valuedness of the action is either related to the hidden topological angle or to the resurgent cancellation of ambiguities. We also show that in the approximate multi-instanton description the integration over the complex quasi-zero mode thimble produces the most salient features of the exact solutions. While exact complex saddles are more difficult to construct in quantum field theory, the relation to the approximate thimble construction suggests that such solutions may be underlying some remarkable features of approximate bion saddles in quantum field theories.

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arXiv2015

Complexified path integrals, exact saddles and supersymmetry

In the context of two illustrative examples from supersymmetric quantum mechanics we show that the semi-classical analysis of the path integral requires complexification of the configuration space and action, and the inclusion of complex saddle points, even when the parameters in the action are real. We find new exact complex saddles, and show that without their contribution the semi-classical expansion is in conflict with basic properties such as positive-semidefiniteness of the spectrum, and constraints of supersymmetry. Generic saddles are not only complex, but also possibly multi-valued, and even singular. This is in contrast to instanton solutions, which are real, smooth, and single-valued. The multi-valuedness of the action can be interpreted as a hidden topological angle, quantized in units of $π$ in supersymmetric theories. The general ideas also apply to non-supersymmetric theories.

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arXiv2015

Strings from domain walls in supersymmetric Yang-Mills theory and adjoint QCD

We study strings between static quarks in QCD with $n_f$ adjoint fermions, including $N=1$ Super Yang-Mills (SYM), in the calculable regime on $\mathbb R^3\times \mathbb S^1$. We find that they have many qualitatively new features not previously known. The difference from other realizations of abelian confinement is due to the composite nature of magnetic bions, whose Dirac quantum with fundamental quarks is two, and to the unbroken part of the Weyl group. In particular we show that strings are composed of two domain walls, that quarks are not confined on domain walls, that strings can end on domain walls, and that "Y" or "$Δ$" baryons can form. We briefly discuss their lightest modes and decompactification limit.

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arXiv2015

Hidden topological angles and Lefschetz thimbles

We demonstrate the existence of hidden topological angles (HTAs) in a large class of quantum field theories and quantum mechanical systems. HTAs are distinct from theta-parameters in the lagrangian. They arise as invariant angle associated with saddle points of the complexified path integral and their descent manifolds (Lefschetz thimbles). Physical effects of HTAs become most transparent upon analytic continuation in $n_f$ to non-integer number of flavors, reducing in the integer $n_f$ limit to a $\mathbb Z_2$ valued phase difference between dominant saddles. In ${\cal N}=1$ super Yang-Mills theory we demonstrate the microscopic mechanism for the vanishing of the gluon condensate. The same effect leads to an anomalously small condensate in a QCD-like $SU(N)$ gauge theory with fermions in the two-index representation. The basic phenomenon is that, contrary to folklore, the gluon condensate can receive both positive and negative contributions in a semi-classical expansion. In quantum mechanics, a HTA leads to a difference in semi-classical expansion of integer and half-integer spin particles.

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arXiv2014

The absence of IR renormalons in gauge theories on $\mathbb R^3\times \mathbb S^1$ and what it means for resurgence

We analyze the renormalon diagram of gauge theories on $\mathbb R^3\times \mathbb S^1$. In particular, we perform exact one loop calculations for the vacuum polarization in QCD with adjoint matter and observe that all infrared logarithms, as functions of the external momentum, cancel between the vacuum part and finite volume part, which eliminates the IR renormalon problem. We argue that the singularities in the Borel plane, arising from the topological neutral bions, are not associated with renormalons, but with the proliferation of the Feynman diagrams. As a byproduct, we obtain, for the first time, an exact one-loop result of the vacuum polarization which can be adapted to the case of thermal compactification of QCD.

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arXiv2014

Nonlinear sigma models at nonzero chemical potential: breaking up instantons and the phase diagram

We consider asymptotically free nonlinear sigma models in two dimensions which, due to their internal symmetries, allow for a conserved charge. Introducing nonzero chemical potential for the SO(2) subgroup of the symmetry group, we discuss two expected phase transitions, which are related to charge condensation and percolation of merons, respectively. The latter are topological objects with half integer charge similar to vortices in the abelianized \emph{O(2)} theory, that emerge for large chemical potentials due to the suppression of the complementary field components. We conjecture a particular ordering of these transitions supported by large N calculations, and discuss dualities helpful for the understanding of these systems in the continuum and on the lattice. In conclusion we suggest that similar behavior is to be expected in QCD at finite density.

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arXiv2013

(S)QCD on R^3 x S^1: Screening of Polyakov loop by fundamental quarks and the demise of semi-classics

Recently, it was argued that the thermal deconfinement transition in pure Yang-Mills theory is continuously connected to a quantum phase transition in softly-broken N=1 SYM theory on R^3 x S^1. The transition is semiclassically calculable at small S^1 size L, occurs as the soft mass m_soft and L vary, and is driven by a competition between perturbative effects and nonperturbative topological molecules. These are correlated instanton--anti-instanton tunneling events, whose constituents are monopole-instantons "bound" by attractive long-range forces. The mechanism driving the transition is universal for all simple gauge groups, with or without a center, such as SU(N) or G_2. Here, we consider theories with fundamental quarks. We examine the role topological objects play in determining the fate of the (exact or approximate) center-symmetry in SU(2) SQCD, with or without soft-breaking terms. In theories whose large-m_soft limit is thermal nonsupersymmetric QCD with massive quarks, we find a crossover of the Polyakov loop, from approximately center-symmetric at small 1/L to maximally center-broken at larger 1/L, as seen in lattice thermal QCD with massive quarks and T=1/L. We argue that in all calculable cases, including SQCD with exact center symmetry, quarks deform instanton-monopoles by their quantum fluctuations and do not contribute to their binding. The semiclassical approximation and the molecular picture of the vacuum fail, upon decreasing the quark mass, precisely when quarks would begin mediating a long-range attractive force between monopole-instantons, calling for a dual description of the resulting strong-coupling theory.

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arXiv2013

Topological zero modes at nonzero chemical potential

We give analytical and numerical solutions for the zero modes of the Dirac operator in topological SU(2) gauge backgrounds at nonzero chemical potential. Continuation from imaginary to real chemical potential is used to systematically derive analytical zero modes for calorons at arbitrary holonomy and, in particular limits, for instantons and dyons (magnetic monopoles). For the latter a spherical ansatz is explored as well. All the zero mode exhibit stronger peaks at the core and negative regions in their densities. We discuss the structure of the corresponding overlap matrix elements. For discretized calorons on the lattice we consider the staggered operator and show that it does possess (quartet quasi-)zero modes, whose eigenmodes agree very well with the continuum profiles, also for nonzero chemical potential.

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arXiv2012

The Chiral Symmetry Breaking/Restoration in Dyonic Vacuum

We discuss the topological phenomena in the QCD-like theories with variable number of fundamental $N_f$ or adjoint $N_a$ fermions, focusing on the temperatures at or above the critical value $T_c$ of chiral symmetry restoration. Nonzero average of the Polyakov line, or holonomy, splits instantons into (anti)selfdual dyons, and we study both bosonic and fermionic interactions between them. The high temperature phase is a dilute gas of "molecules" made of $2N_c$ dyons, neutral in topological, electric and magnetic charges. At intermediate temperatures the diluteness reaches some critical level at which chiral symmetry gets restored: we explain why it is very different for the fundamental and adjoint fermions. At high density the ensemble is a strongly coupled liquid with crystal-like short range order: we speculate about its structure at small and large $N_f$. We finally explaine certain lattice observations and suggest a number of further lattice tests.

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