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Wenbin Yan - One of the best experts on this subject based on the ideXlab platform.
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vertex operator algebras of argyres douglas theories from m5 branes
Journal of High Energy Physics, 2017Co-Authors: Jaewon Song, Dan Xie, Wenbin YanAbstract:We study aspects of the vertex operator algebra (VOA) corresponding to Argyres-Douglas (AD) theories engineered using the 6d $$ \mathcal{N}=\left(2,\ 0\right) $$ theory of type J on a punctured sphere. We denote the AD theories as (J b [k], Y), where J b [k] and Y represent an irRegular and a Regular Singularity respectively. We restrict to the ‘minimal’ case where J b [k] has no associated mass parameters, and the theory does not admit any exactly marginal deformations. The VOA corresponding to the AD theory is conjectured to be the W-algebra $$ {\mathcal{W}}^{k_{2d}}\left(J,\ Y\ \right) $$ , where $$ {k}_{2d}=-h+\frac{b}{b+k} $$ with h being the dual Coxeter number of J. We verify this conjecture by showing that the Schur index of the AD theory is identical to the vacuum character of the corresponding VOA, and the Hall-Littlewood index computes the Hilbert series of the Higgs branch. We also find that the Schur and Hall-Littlewood index for the AD theory can be written in a simple closed form for b = h. We also test the conjecture that the associated variety of such VOA is identical to the Higgs branch. The M5-brane construction of these theories and the corresponding TQFT structure of the index play a crucial role in our computations.
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vertex operator algebras of argyres douglas theories from m5 branes
arXiv: High Energy Physics - Theory, 2017Co-Authors: Jaewon Song, Dan Xie, Wenbin YanAbstract:We study aspects of the vertex operator algebra (VOA) corresponding to Argyres-Douglas (AD) theories engineered using the 6d N=(2, 0) theory of type $J$ on a punctured sphere. We denote the AD theories as $(J^b[k],Y)$, where $J^b[k]$ and $Y$ represent an irRegular and a Regular Singularity respectively. We restrict to the `minimal' case where $J^b[k]$ has no associated mass parameters, and the theory does not admit any exactly marginal deformations. The VOA corresponding to the AD theory is conjectured to be the W-algebra $\mathcal{W}^{k_{2d}}(J,Y)$, where $k_{2d}=-h+ \frac{b}{b+k}$ with $h$ being the dual Coxeter number of $J$. We verify this conjecture by showing that the Schur index of the AD theory is identical to the vacuum character of the corresponding VOA, and the Hall-Littlewood index computes the Hilbert series of the Higgs branch. We also find that the Schur and Hall-Littlewood index for the AD theory can be written in a simple closed form for $b=h$. We also test the conjecture that the associated variety of such VOA is identical to the Higgs branch. The M5-brane construction of these theories and the corresponding TQFT structure of the index play a crucial role in our computations.
Jaewon Song - One of the best experts on this subject based on the ideXlab platform.
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vertex operator algebras of argyres douglas theories from m5 branes
Journal of High Energy Physics, 2017Co-Authors: Jaewon Song, Dan Xie, Wenbin YanAbstract:We study aspects of the vertex operator algebra (VOA) corresponding to Argyres-Douglas (AD) theories engineered using the 6d $$ \mathcal{N}=\left(2,\ 0\right) $$ theory of type J on a punctured sphere. We denote the AD theories as (J b [k], Y), where J b [k] and Y represent an irRegular and a Regular Singularity respectively. We restrict to the ‘minimal’ case where J b [k] has no associated mass parameters, and the theory does not admit any exactly marginal deformations. The VOA corresponding to the AD theory is conjectured to be the W-algebra $$ {\mathcal{W}}^{k_{2d}}\left(J,\ Y\ \right) $$ , where $$ {k}_{2d}=-h+\frac{b}{b+k} $$ with h being the dual Coxeter number of J. We verify this conjecture by showing that the Schur index of the AD theory is identical to the vacuum character of the corresponding VOA, and the Hall-Littlewood index computes the Hilbert series of the Higgs branch. We also find that the Schur and Hall-Littlewood index for the AD theory can be written in a simple closed form for b = h. We also test the conjecture that the associated variety of such VOA is identical to the Higgs branch. The M5-brane construction of these theories and the corresponding TQFT structure of the index play a crucial role in our computations.
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vertex operator algebras of argyres douglas theories from m5 branes
arXiv: High Energy Physics - Theory, 2017Co-Authors: Jaewon Song, Dan Xie, Wenbin YanAbstract:We study aspects of the vertex operator algebra (VOA) corresponding to Argyres-Douglas (AD) theories engineered using the 6d N=(2, 0) theory of type $J$ on a punctured sphere. We denote the AD theories as $(J^b[k],Y)$, where $J^b[k]$ and $Y$ represent an irRegular and a Regular Singularity respectively. We restrict to the `minimal' case where $J^b[k]$ has no associated mass parameters, and the theory does not admit any exactly marginal deformations. The VOA corresponding to the AD theory is conjectured to be the W-algebra $\mathcal{W}^{k_{2d}}(J,Y)$, where $k_{2d}=-h+ \frac{b}{b+k}$ with $h$ being the dual Coxeter number of $J$. We verify this conjecture by showing that the Schur index of the AD theory is identical to the vacuum character of the corresponding VOA, and the Hall-Littlewood index computes the Hilbert series of the Higgs branch. We also find that the Schur and Hall-Littlewood index for the AD theory can be written in a simple closed form for $b=h$. We also test the conjecture that the associated variety of such VOA is identical to the Higgs branch. The M5-brane construction of these theories and the corresponding TQFT structure of the index play a crucial role in our computations.
Clemens Markett - One of the best experts on this subject based on the ideXlab platform.
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properties of the solutions of the fourth order bessel type differential equation
Journal of Mathematical Analysis and Applications, 2009Co-Authors: W N Everitt, Clemens Markett, L L LittlejohnAbstract:The structured Bessel-type functions of arbitrary even-order were introduced by Everitt and Markett in 1994; these functions satisfy linear ordinary differential equations of the same even-order. The differential equations have analytic coefficients and are defined on the whole complex plane with a Regular Singularity at the origin and an irRegular Singularity at the point of infinity. They are all natural extensions of the classical second-order Bessel differential equation. Further these differential equations have real-valued coefficients on the positive real half-line of the plane, and can be written in Lagrange symmetric (formally self-adjoint) form. In the fourth-order case, the Lagrange symmetric differential expression generates self-adjoint unbounded operators in certain Hilbert function spaces. These results are recorded in many of the papers here given as references. It is shown in the original paper of 1994 that in this fourth-order case one solution exists which can be represented in terms of the classical Bessel functions of order 0 and 1. The existence of this solution, further aided by computer programs in Maple, led to the existence of a linearly independent basis of solutions of the differential equation. In this paper a new proof of the existence of this solution base is given, on using the advanced theory of special functions in the complex plane. The methods lead to the development of analytical properties of these solutions, in particular the series expansions of all solutions at the Regular Singularity at the origin of the complex plane.
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the fourth order bessel type differential equation
Applicable Analysis, 2004Co-Authors: Jyoti Das, W N Everitt, D B Hinton, L L Littlejohn, Clemens MarkettAbstract:The Bessel-type functions, structured as extensions of the classical Bessel functions, were defined by Everitt and Markett in 1994. These special functions are derived by linear combinations and limit processes from the classical orthogonal polynomials, classical Bessel functions and the Krall Jacobi-type and Laguerre-type orthogonal polynomials. These Bessel-type functions are solutions of higher-order linear differential equations, with a Regular Singularity at the origin and an irRegular Singularity at the point of infinity of the complex plane. There is a Bessel-type differential equation for each even-order integer; the equation of order two is the classical Bessel differential equation. These even-order Bessel-type equations are not formal powers of the classical Bessel equation. When the independent variable of these equations is restricted to the positive real axis of the plane they can be written in the Lagrange symmetric (formally self-adjoint) form of the Glazman–Naimark type, with real coeffic...
L L Littlejohn - One of the best experts on this subject based on the ideXlab platform.
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properties of the solutions of the fourth order bessel type differential equation
Journal of Mathematical Analysis and Applications, 2009Co-Authors: W N Everitt, Clemens Markett, L L LittlejohnAbstract:The structured Bessel-type functions of arbitrary even-order were introduced by Everitt and Markett in 1994; these functions satisfy linear ordinary differential equations of the same even-order. The differential equations have analytic coefficients and are defined on the whole complex plane with a Regular Singularity at the origin and an irRegular Singularity at the point of infinity. They are all natural extensions of the classical second-order Bessel differential equation. Further these differential equations have real-valued coefficients on the positive real half-line of the plane, and can be written in Lagrange symmetric (formally self-adjoint) form. In the fourth-order case, the Lagrange symmetric differential expression generates self-adjoint unbounded operators in certain Hilbert function spaces. These results are recorded in many of the papers here given as references. It is shown in the original paper of 1994 that in this fourth-order case one solution exists which can be represented in terms of the classical Bessel functions of order 0 and 1. The existence of this solution, further aided by computer programs in Maple, led to the existence of a linearly independent basis of solutions of the differential equation. In this paper a new proof of the existence of this solution base is given, on using the advanced theory of special functions in the complex plane. The methods lead to the development of analytical properties of these solutions, in particular the series expansions of all solutions at the Regular Singularity at the origin of the complex plane.
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the fourth order bessel type differential equation
Applicable Analysis, 2004Co-Authors: Jyoti Das, W N Everitt, D B Hinton, L L Littlejohn, Clemens MarkettAbstract:The Bessel-type functions, structured as extensions of the classical Bessel functions, were defined by Everitt and Markett in 1994. These special functions are derived by linear combinations and limit processes from the classical orthogonal polynomials, classical Bessel functions and the Krall Jacobi-type and Laguerre-type orthogonal polynomials. These Bessel-type functions are solutions of higher-order linear differential equations, with a Regular Singularity at the origin and an irRegular Singularity at the point of infinity of the complex plane. There is a Bessel-type differential equation for each even-order integer; the equation of order two is the classical Bessel differential equation. These even-order Bessel-type equations are not formal powers of the classical Bessel equation. When the independent variable of these equations is restricted to the positive real axis of the plane they can be written in the Lagrange symmetric (formally self-adjoint) form of the Glazman–Naimark type, with real coeffic...
P A G Pisani - One of the best experts on this subject based on the ideXlab platform.
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krein s formula and heat kernel expansion for some differential operators with a Regular Singularity
arXiv: Mathematical Physics, 2005Co-Authors: H Falomir, P A G PisaniAbstract:We get a generalization of Krein's formula -which relates the resolvents of different selfadjoint extensions of a differential operator with Regular coefficients- to the non-Regular case $A=-\partial_x^2+(\nu^2-1/4)/x^2+V(x)$, where $0<\nu<1$ and $V(x)$ is an analytic function of $x\in\mathbb{R}^+$ bounded from below. We show that the trace of the heat-kernel $e^{-tA}$ admits a non-standard small-t asymptotic expansion which contains, in general, integer powers of $t^\nu$. In particular, these powers are present for those selfadjoint extensions of $A$ which are characterized by boundary conditions that break the local formal scale invariance at the Singularity.
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on the resolvent and spectral functions of a second order differential operator with a Regular Singularity
Journal of Mathematical Physics, 2004Co-Authors: H Falomir, M A Muschietti, P A G PisaniAbstract:We consider the resolvent of a second order differential operator with a Regular Singularity, admitting a family of self-adjoint extensions. We find that the asymptotic expansion for the resolvent in the general case presents unusual powers of λ which depend on the Singularity. The consequences for the pole structure of the ζ function, and for the small-t asymptotic expansion of the heat kernel, are also discussed.
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on the resolvent and spectral functions of a second order differential operator with a Regular Singularity
arXiv: Mathematical Physics, 2004Co-Authors: H Falomir, M A Muschietti, P A G PisaniAbstract:We consider the resolvent of a second order differential operator with a Regular Singularity, admitting a family of self-adjoint extensions. We find that the asymptotic expansion for the resolvent in the general case presents unusual powers of $\lambda$ which depend on the Singularity. The consequences for the pole structure of the $\zeta$-function, and the small-$t$ asymptotic expansion of the heat-kernel, are also discussed.