PARTITION FUNCTIONS OF THE SUPERCONFORMAL GHOST THIRRING MODEL

1989 ◽  
Vol 04 (20) ◽  
pp. 5553-5574 ◽  
Author(s):  
D. Z. FREEDMAN ◽  
K. PILCH
Keyword(s):  
Energy Spectrum ◽  
Path Integral ◽  
Formal Series ◽  
Open String ◽  
Integral Representations ◽  
Thirring Model ◽  
Partition Functions ◽  
First Order ◽  
Integral Methods ◽  
The One

The one-loop partition functions of the superconformal Thirring model for first order b − c and β − γ ghost fields are studied for both closed and open string boundary conditions. Bosonized partition functions are given by formal series which usually diverge because the energy spectrum of the theory is unbounded below as a correlate of nonunitarity. However, the same partition functions are then calculated by path integral methods directly in the fermionic formulation, and well-defined (convergent) integral representations are obtained. A formal series expansion of those integrals reproduces the bosonized partition functions.

Dirac oscillator in a uniform electric field: Path integral treatment

2019 ◽  
Vol 34 (30) ◽  
pp. 1950246
Author(s):  
Hassene Bada ◽  
Mekki Aouachria
Keyword(s):  
Energy Spectrum ◽  
Electric Field ◽  
Path Integral ◽  
Uniform Electric Field ◽  
Two Dimensional ◽  
Dirac Oscillator ◽  
Fermionic Model ◽  
Internal Motions ◽  
Integral Treatment ◽  
The One

In this paper, the propagator of a two-dimensional Dirac oscillator in the presence of a uniform electric field is derived by using the path integral technique. The fact that the globally named approach is used in this work redirects, beforehand, our search for the propagator of the Dirac equation to that of the propagator of its quadratic form. The internal motions relative to the spin are represented by two fermionic oscillators, which are described by Grassmannian variables, according to Schwinger’s fermionic model. Once the integration over the anticommuting variables (Grassmannian variables) is accomplished, the problem becomes the one of finding a non-relativistic propagator with only bosonic variables. The energy spectrum of the electron and the corresponding eigenspinors are also obtained in this work.

scholarly journals Comments on open string with ‘massive’ boundary term

2020 ◽  
Vol 476 (2236) ◽  
pp. 20190748
Author(s):  
Arkady A. Tseytlin
Keyword(s):  
Scattering Amplitudes ◽  
Partition Function ◽  
Gauge Field ◽  
Path Integral ◽  
Open String ◽  
One Dimensional ◽  
Conformally Invariant ◽  
Additional Constant ◽  
The One ◽  
Definition Of

We discuss possible definition of open string path integral in the presence of additional boundary couplings corresponding to the presence of masses at the ends of the string. These couplings are not conformally invariant implying that as in a non-critical string case one is to integrate over the one-dimensional metric or reparametrizations of the boundary. We compute the partition function on the disc in the presence of an additional constant gauge field background and comment on the structure of the corresponding scattering amplitudes.

scholarly journals PATH INTEGRAL REPRESENTATION FOR INTERFACE STATES OF THE ANISOTROPIC HEISENBERG MODEL

2000 ◽  
Vol 12 (10) ◽  
pp. 1325-1344 ◽  
Author(s):  
OSCAR BOLINA ◽  
PIERLUIGI CONTUCCI ◽  
BRUNO NACHTERGAELE
Keyword(s):  
Integral Representation ◽  
Path Integral ◽  
Two Dimensions ◽  
Integral Model ◽  
Partition Functions ◽  
Translation Invariant ◽  
Xxz Model ◽  
Path Integral Representation ◽  
Ferromagnetic Chain ◽  
The One

We develop a geometric representation for the ground state of the spin-1/2 quantum XXZ ferromagnetic chain in terms of suitably weighted random walks in a two-dimensional lattice. The path integral model so obtained admits a genuine classical statistical mechanics interpretation with a translation invariant Hamiltonian. This new representation is used to study the interface ground states of the XXZ model. We prove that the probability of having a number of down spins in the up phase decays exponentially with the sum of their distances to the interface plus the square of the number of down spins. As an application of this bound, we prove that the total third component of the spin in a large interval of even length centered on the interface does not fluctuate, i.e. has zero variance. We also show how to construct a path integral representation in higher dimensions and obtain a reduction formula for the partition functions in two dimensions in terms of the partition function of the one-dimensional model.

ABELIAN BOSONIZATION IN A PATH INTEGRAL FRAMEWORK

1993 ◽  
Vol 08 (11) ◽  
pp. 1923-1931 ◽  
Author(s):  
TH. JOLICŒUR ◽  
J. C. LE GUILLOU
Keyword(s):  
Path Integral ◽  
Correlation Functions ◽  
Thirring Model ◽  
Integral Formulation ◽  
Partition Functions ◽  
Path Integral Formulation ◽  
Schwinger Model

We investigate the Abelian bosonization procedure in the light of a path integral formulation. The correlation functions of the Bose and Fermi fields are directly related by use of several changes of variables including chiral rotations à la Fujikawa. Operator identities are replaced by statements on partition functions with suitably defined sources. The Thirring and sine–Gordon models as well as the Schwinger model are treated. We also discuss a generalized Thirring model.

scholarly journals PATH INTEGRAL REPRESENTATION FOR SCHRÖDINGER OPERATORS WITH BERNSTEIN FUNCTIONS OF THE LAPLACIAN

2012 ◽  
Vol 24 (06) ◽  
pp. 1250013 ◽  
Author(s):  
FUMIO HIROSHIMA ◽  
TAKASHI ICHINOSE ◽  
JÓZSEF LŐRINCZI
Keyword(s):  
Brownian Motion ◽  
Path Integral ◽  
Schrödinger Operators ◽  
Integral Representations ◽  
Schrodinger Operators ◽  
Kato Class ◽  
Path Integral Representation ◽  
Bernstein Functions ◽  
Subordinate Brownian Motion ◽  
The One

Path integral representations for generalized Schrödinger operators obtained under a class of Bernstein functions of the Laplacian are established. The one-to-one correspondence of Bernstein functions with Lévy subordinators is used, thereby the role of Brownian motion entering the standard Feynman–Kac formula is taken here by subordinate Brownian motion. As specific examples, fractional and relativistic Schrödinger operators with magnetic field and spin are covered. Results on self-adjointness of these operators are obtained under conditions allowing for singular magnetic fields and singular external potentials as well as arbitrary integer and half-integer spin values. This approach also allows to propose a notion of generalized Kato class for which an Lp-Lq bound of the associated generalized Schrödinger semigroup is shown. As a consequence, diamagnetic and energy comparison inequalities are also derived.

Approximate path integral methods for partition functions

1993 ◽  
Vol 98 (5) ◽  
pp. 4120-4127 ◽  
Author(s):  
Michael Messina ◽  
Gregory K. Schenter ◽  
Bruce C. Garrett
Keyword(s):  
Path Integral ◽  
Partition Functions ◽  
Integral Methods

THE HUBBARD OPERATORS AND THE SLAVE-PARTICLES PATH-INTEGRAL REPRESENTATIONS DESCRIBING THE t-J MODEL

2007 ◽  
Vol 21 (11) ◽  
pp. 1861-1874
Author(s):  
O. S. ZANDRON
Keyword(s):  
Path Integral ◽  
Integral Representations ◽  
Symplectic Method ◽  
Generating Functional ◽  
First Order ◽  
The Family ◽  
Hubbard Operators

In the present work it is shown that the family of first-order Lagrangians for the t-J model and the corresponding correlation generating functional previously found can be exactly mapped into the slave-fermion decoupled representation. Next, by means of the Faddeev-Jackiw symplectic method, a different family of Lagrangians is constructed and it is shown how the corresponding correlation generating functional can be mapped into the slave-boson decoupled representation.

scholarly journals VACUUM PROPERTIES OF A NONLOCAL THIRRING-LIKE MODEL

1998 ◽  
Vol 13 (07) ◽  
pp. 1169-1189 ◽  
Author(s):  
D. G. BARCI ◽  
C. M. NAÓN
Keyword(s):  
Path Integral ◽  
Ground State ◽  
Thirring Model ◽  
Long Distance ◽  
State Wave ◽  
Integral Methods ◽  
Exact Ground State ◽  
Distance Behavior

We use path-integral methods to analyze the vacuum properties of a recently proposed extension of the Thirring model in which the interaction between fermionic currents is nonlocal. We calculate the exact ground state wave functional of the model for any bilocal potential, and also study its long-distance behavior. We show that the ground state wave functional has a general factored Jastrow form. We also find that it possesses an interesting symmetry involving the interchange of density–density and current–current interactions.

scholarly journals Gauge theories on compact toric manifolds

2021 ◽  
Vol 111 (3) ◽  
Author(s):  
Giulio Bonelli ◽  
Francesco Fucito ◽  
Jose Francisco Morales ◽  
Massimiliano Ronzani ◽  
Ekaterina Sysoeva ◽  
...  
Keyword(s):  
Partition Function ◽  
Gauge Theories ◽  
Blow Up ◽  
Gauge Coupling ◽  
Piecewise Constant Function ◽  
Partition Functions ◽  
Piecewise Constant ◽  
Toric Manifolds ◽  
Holomorphic Anomaly ◽  
The One

AbstractWe compute the $$\mathcal{N}=2$$ N = 2 supersymmetric partition function of a gauge theory on a four-dimensional compact toric manifold via equivariant localization. The result is given by a piecewise constant function of the Kähler form with jumps along the walls where the gauge symmetry gets enhanced. The partition function on such manifolds is written as a sum over the residues of a product of partition functions on $$\mathbb {C}^2$$ C 2 . The evaluation of these residues is greatly simplified by using an “abstruse duality” that relates the residues at the poles of the one-loop and instanton parts of the $$\mathbb {C}^2$$ C 2 partition function. As particular cases, our formulae compute the SU(2) and SU(3) equivariant Donaldson invariants of $$\mathbb {P}^2$$ P 2 and $$\mathbb {F}_n$$ F n and in the non-equivariant limit reproduce the results obtained via wall-crossing and blow up methods in the SU(2) case. Finally, we show that the U(1) self-dual connections induce an anomalous dependence on the gauge coupling, which turns out to satisfy a $$\mathcal {N}=2$$ N = 2 analog of the $$\mathcal {N}=4$$ N = 4 holomorphic anomaly equations.

scholarly journals Twisted 6d (2, 0) SCFTs on a circle

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Zhihao Duan ◽  
Kimyeong Lee ◽  
June Nahmgoong ◽  
Xin Wang
Keyword(s):  
Lie Groups ◽  
Point Of View ◽  
Partition Functions ◽  
Congruence Subgroups ◽  
Gauge Groups ◽  
Simple Lie Groups ◽  
Instanton Contribution ◽  
Elliptic Genera ◽  
Supersymmetric Gauge ◽  
The One

Abstract We study twisted circle compactification of 6d (2, 0) SCFTs to 5d $$ \mathcal{N} $$ N = 2 supersymmetric gauge theories with non-simply-laced gauge groups. We provide two complementary approaches towards the BPS partition functions, reflecting the 5d and 6d point of view respectively. The first is based on the blowup equations for the instanton partition function, from which in particular we determine explicitly the one-instanton contribution for all simple Lie groups. The second is based on the modular bootstrap program, and we propose a novel modular ansatz for the twisted elliptic genera that transform under the congruence subgroups Γ0(N) of SL(2, ℤ). We conjecture a vanishing bound for the refined Gopakumar-Vafa invariants of the genus one fibered Calabi-Yau threefolds, upon which one can determine the twisted elliptic genera recursively. We use our results to obtain the 6d Cardy formulas and find universal behaviour for all simple Lie groups. In addition, the Cardy formulas remain invariant under the twist once the normalization of the compact circle is taken into account.

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