Summary: We study the non-perturbative Coulomb phase of $D=6$, $N=1$ heterotic string vacua with ... more Summary: We study the non-perturbative Coulomb phase of $D=6$, $N=1$ heterotic string vacua with more than one tensor multiplet. We find that, for $n_T>9$, the Coulomb branch is divided by a codimension-one hypersurface, across which the coupling of gravitational curvature-squared term changes sign. We find a new class of BPS soliton strings whose core is supported by a gravitational instanton, i.e. a self-dual gravitational string. For $n_T>9$, tension of the string vanishes at a codimension-one hypersurface. We suggest that the tensionless gravitational string might be related to a novel infrared phase of quantum gravity
M(atrix) theory compactified on an orbifold ${\bf T}_9/{\bf Z}_2$ is studied. Via zero-brane part... more M(atrix) theory compactified on an orbifold ${\bf T}_9/{\bf Z}_2$ is studied. Via zero-brane parton scattering we find that each of the 254 orbifold fixed points carry -1/32 units of zero-brane charge. The anomalous flux is cancelled by introducing a twisted sector consisting of 32 zero-branes that are spacetime supersymmetry singlets. These twisted sector zero-branes are nothing but gravitational waves propagating along the M-theory direction. There is no D0-partons in the untwisted sector, a fact consistent with holographic principle. For low-energy excitations, the orbifold compactification is described by ten-dimensional supersymmetric Yang-Mills theory with gauge group SO(32)
M(atrix) theory description is investigated for M-theory compactified on non-orientable manifolds... more M(atrix) theory description is investigated for M-theory compactified on non-orientable manifolds. Relevant M(atrix) theory is obtained by Fourier transformation in a way consistent with T-duality. For nine-dimensional compactification on Klein bottle and M\"obius strip, we show that M(atrix) theory is (2+1)-dimensional ${\cal N} = 8$ supersymmetric U(N) gauge theory defined on dual Klein bottle and dual Moebius strip parameter space
Abstract: We study the physics of multiple M5-branes compactified on a hyperbolic 3-manifold. On ... more Abstract: We study the physics of multiple M5-branes compactified on a hyperbolic 3-manifold. On the one hand, it leads to the 3d-3d correspondence which maps an N = 2 superconformal field theory to a pure Chern-Simons theory on the 3-manifold. On the other hand, it leads to a warped AdS4 geometry in M-theory holographically dual to the superconformal field theory. Combining the holographic duality and the 3d-3d correspon-dence, we propose a conjecture for the large N limit of the perturbative free energy of a Chern-Simons theory on hyperbolic 3-manifold. The conjecture claims that the tree, one-loop and two-loop terms all share the same N3 scaling behavior and are proportional to the volume of the 3-manifold, while the three-loop and higher terms are suppressed at large N. Under mild assumptions, we prove the tree and one-loop parts of the conjecture. For the two-loop part, we test the conjecture numerically in a number of examples and find precise agreement. We also confirm the su...
We study D-brane bound states with a non-Abelian background on noncommutative T. We construct twi... more We study D-brane bound states with a non-Abelian background on noncommutative T. We construct twisted quantum bundles and adjoint sections describing D-brane bound states. It is shown that the noncommutative T with non-Abelian backgrounds also exhibits SO(4, 4|Z) duality and the action of this group gives Morita equivalent T on which only D0-branes exist. For a reducible non-Abelian background, the moduli space of D-brane bound states in Type II string theory takes the form ∏ a(T )/Sqa .
We study the large-N limit of superconformal index for two strongly interacting Chern-Simons theo... more We study the large-N limit of superconformal index for two strongly interacting Chern-Simons theories in three dimensions with $$ \mathcal{N} $$ N = 2 supersymmetry, and compare the result against the AdS/CFT dual, namely the data of full Kaluza-Klein reduction spectra obtained using the exceptional field theory technique. The two theories of interest are mABJM and GJV theories, which are obtained as IR fixed point of RG whose UV description is ABJM and maximally supersymmetric Yang-Mills theory respectively. We confirm agreement and the duality persists. For the case of mABJM it turns out that we need a refinement of the gravity index which reflects the fact that the UV description on the field theory side has enhanced global symmetry.
We study the Hamilton-Jacobi formulation of effective mechanical actions associated with holograp... more We study the Hamilton-Jacobi formulation of effective mechanical actions associated with holographic renormalization group flows when the field theory is put on the sphere and mass terms are turned on. Although the system is supersymmetric and it is described by a superpotential, Hamilton’s characteristic function is not readily given by the superpotential when the boundary of AdS is curved. We propose a method to construct the solution as a series expansion in scalar field degrees of freedom. The coefficients are functions of the warp factor to be determined by a differential equation one obtains when the ansatz is substituted into the Hamilton-Jacobi equation. We also show how the solution can be derived from the BPS equations without having to solve differential equations. The characteristic function readily provides information on holographic counterterms which cancel divergences of the on-shell action near the boundary of AdS.
We study the large N sign oscillation of the twisted indices for 3D theories of class ℛ obtained ... more We study the large N sign oscillation of the twisted indices for 3D theories of class ℛ obtained from M5-branes wrapped on a hyperbolic 3-manifold. Holographically, the oscillatory behavior can be understood from the imaginary part of on-shell actions for the two Euclidean supergravity solutions, Bolt± with p = 0, which are Wick rotation of magnetically charged AdS4 black holes. The two solutions have the same imaginary part with opposite sign. The imaginary part comes from the F ∧ F-term in the supergravity and the coefficient is proportional to the Chern-Simons invariant of 3-manifold. Combining the holographic computation with 3D-3D relation for twisted indices, we propose a non-trivial mathematical conjecture regarding the phase factor of a twisted Reidemeister-Ray-Singer torsion on hyperbolic 3-manifold.
We revisit non-rotating, dyonically charged, and supersymmetric AdS4 black holes, which are solut... more We revisit non-rotating, dyonically charged, and supersymmetric AdS4 black holes, which are solutions of $$ \mathcal{N} $$ N = 2 gauged supergravity with vector- and hyper-multiplets. Uplifting the near horizon solutions to D = 11 supergravity on seven-dimensional Sasaki-Einstein manifolds, we show that dyonic AdS4 black holes correspond to AdS2 solutions with electric and magnetic baryonic fluxes in D = 11 supergravity. We identify the off-shell AdS4 black hole solutions with parameters of D = 11 AdS2 solutions without imposing the equations of motion. We calculate the entropy of dyonic black holes, carefully analyzing the Page charge quantization conditions.
We revisit the stringy construction of four-dimensional de-Sitter solutions using orientifolds O8... more We revisit the stringy construction of four-dimensional de-Sitter solutions using orientifolds O8±, proposed by Córdova et al. (2019) [1]. While the original analysis of the supergravity equations is largely numerical, we obtain semi-analytic solutions by treating the curvature as a perturbative parameter. At each order we verify that the (permissive) boundary conditions at the orientifolds are satisfied. To illustrate the advantage of our result, we calculate the four-dimensional Newton constant as a function of the cosmological constant. We also discuss how the discontinuities at O8− can be accounted for in terms of corrections to the worldvolume action.
Recently it was discovered that twisted superconformal index $$ \mathcal{I} $$ I can be used to u... more Recently it was discovered that twisted superconformal index $$ \mathcal{I} $$ I can be used to understand the Bekenstein-Hawking entropy of magnetically charged black holes in AdS spacetime. In this paper we apply the so-called $$ \mathcal{I} $$ I -extremization procedure to three-dimensional gauge field theories and their geometric dual, focusing in particular on the seven-dimensional Sasaki-Einstein manifold M 1,1,1. We generalize recent studies on relations among toric geometry, variational principles, and black hole entropy to the case of AdS2 × Y 9, where Y 9 is a fibration of toric Sasaki-Einstein manifold M 1,1,1 over a two-dimensional Riemann surface Σ g . The nine-dimensional variational problem is given in terms of an entropy functional. In order to illustrate the computations as explicitly as possible, we consider cases where either only mesonic or baryonic fluxes are turned on. By employing the operator counting method, we calculate the S 3 free energy and the topologic...
We study supergravity BPS equations which correspond to mass-deformation of some representative A... more We study supergravity BPS equations which correspond to mass-deformation of some representative AdS/CFT examples. The field theory of interest are $$ \mathcal{N} $$ N = 4, D = 4 super Yang-Mills, the ABJM model in D = 3, and the Brandhuber-Oz fixed point in D = 5. For these gauge theories the free energy with mass terms for matter multiplets is calculable in large-N limit using supersymmetric localization technique. We suggest a perturbative method to solve the supergravity equations. For the dual of mass-deformed ABJM model we reproduce the known exact solutions. For the mass-deformed Brandhuber-Oz theory our method gives the holographic free energy in analytic form. For $$ \mathcal{N} $$ N = 2* theory our result is in good agreement with the localization result.
Summary: We study the non-perturbative Coulomb phase of $D=6$, $N=1$ heterotic string vacua with ... more Summary: We study the non-perturbative Coulomb phase of $D=6$, $N=1$ heterotic string vacua with more than one tensor multiplet. We find that, for $n_T>9$, the Coulomb branch is divided by a codimension-one hypersurface, across which the coupling of gravitational curvature-squared term changes sign. We find a new class of BPS soliton strings whose core is supported by a gravitational instanton, i.e. a self-dual gravitational string. For $n_T>9$, tension of the string vanishes at a codimension-one hypersurface. We suggest that the tensionless gravitational string might be related to a novel infrared phase of quantum gravity
M(atrix) theory compactified on an orbifold ${\bf T}_9/{\bf Z}_2$ is studied. Via zero-brane part... more M(atrix) theory compactified on an orbifold ${\bf T}_9/{\bf Z}_2$ is studied. Via zero-brane parton scattering we find that each of the 254 orbifold fixed points carry -1/32 units of zero-brane charge. The anomalous flux is cancelled by introducing a twisted sector consisting of 32 zero-branes that are spacetime supersymmetry singlets. These twisted sector zero-branes are nothing but gravitational waves propagating along the M-theory direction. There is no D0-partons in the untwisted sector, a fact consistent with holographic principle. For low-energy excitations, the orbifold compactification is described by ten-dimensional supersymmetric Yang-Mills theory with gauge group SO(32)
M(atrix) theory description is investigated for M-theory compactified on non-orientable manifolds... more M(atrix) theory description is investigated for M-theory compactified on non-orientable manifolds. Relevant M(atrix) theory is obtained by Fourier transformation in a way consistent with T-duality. For nine-dimensional compactification on Klein bottle and M\"obius strip, we show that M(atrix) theory is (2+1)-dimensional ${\cal N} = 8$ supersymmetric U(N) gauge theory defined on dual Klein bottle and dual Moebius strip parameter space
Abstract: We study the physics of multiple M5-branes compactified on a hyperbolic 3-manifold. On ... more Abstract: We study the physics of multiple M5-branes compactified on a hyperbolic 3-manifold. On the one hand, it leads to the 3d-3d correspondence which maps an N = 2 superconformal field theory to a pure Chern-Simons theory on the 3-manifold. On the other hand, it leads to a warped AdS4 geometry in M-theory holographically dual to the superconformal field theory. Combining the holographic duality and the 3d-3d correspon-dence, we propose a conjecture for the large N limit of the perturbative free energy of a Chern-Simons theory on hyperbolic 3-manifold. The conjecture claims that the tree, one-loop and two-loop terms all share the same N3 scaling behavior and are proportional to the volume of the 3-manifold, while the three-loop and higher terms are suppressed at large N. Under mild assumptions, we prove the tree and one-loop parts of the conjecture. For the two-loop part, we test the conjecture numerically in a number of examples and find precise agreement. We also confirm the su...
We study D-brane bound states with a non-Abelian background on noncommutative T. We construct twi... more We study D-brane bound states with a non-Abelian background on noncommutative T. We construct twisted quantum bundles and adjoint sections describing D-brane bound states. It is shown that the noncommutative T with non-Abelian backgrounds also exhibits SO(4, 4|Z) duality and the action of this group gives Morita equivalent T on which only D0-branes exist. For a reducible non-Abelian background, the moduli space of D-brane bound states in Type II string theory takes the form ∏ a(T )/Sqa .
We study the large-N limit of superconformal index for two strongly interacting Chern-Simons theo... more We study the large-N limit of superconformal index for two strongly interacting Chern-Simons theories in three dimensions with $$ \mathcal{N} $$ N = 2 supersymmetry, and compare the result against the AdS/CFT dual, namely the data of full Kaluza-Klein reduction spectra obtained using the exceptional field theory technique. The two theories of interest are mABJM and GJV theories, which are obtained as IR fixed point of RG whose UV description is ABJM and maximally supersymmetric Yang-Mills theory respectively. We confirm agreement and the duality persists. For the case of mABJM it turns out that we need a refinement of the gravity index which reflects the fact that the UV description on the field theory side has enhanced global symmetry.
We study the Hamilton-Jacobi formulation of effective mechanical actions associated with holograp... more We study the Hamilton-Jacobi formulation of effective mechanical actions associated with holographic renormalization group flows when the field theory is put on the sphere and mass terms are turned on. Although the system is supersymmetric and it is described by a superpotential, Hamilton’s characteristic function is not readily given by the superpotential when the boundary of AdS is curved. We propose a method to construct the solution as a series expansion in scalar field degrees of freedom. The coefficients are functions of the warp factor to be determined by a differential equation one obtains when the ansatz is substituted into the Hamilton-Jacobi equation. We also show how the solution can be derived from the BPS equations without having to solve differential equations. The characteristic function readily provides information on holographic counterterms which cancel divergences of the on-shell action near the boundary of AdS.
We study the large N sign oscillation of the twisted indices for 3D theories of class ℛ obtained ... more We study the large N sign oscillation of the twisted indices for 3D theories of class ℛ obtained from M5-branes wrapped on a hyperbolic 3-manifold. Holographically, the oscillatory behavior can be understood from the imaginary part of on-shell actions for the two Euclidean supergravity solutions, Bolt± with p = 0, which are Wick rotation of magnetically charged AdS4 black holes. The two solutions have the same imaginary part with opposite sign. The imaginary part comes from the F ∧ F-term in the supergravity and the coefficient is proportional to the Chern-Simons invariant of 3-manifold. Combining the holographic computation with 3D-3D relation for twisted indices, we propose a non-trivial mathematical conjecture regarding the phase factor of a twisted Reidemeister-Ray-Singer torsion on hyperbolic 3-manifold.
We revisit non-rotating, dyonically charged, and supersymmetric AdS4 black holes, which are solut... more We revisit non-rotating, dyonically charged, and supersymmetric AdS4 black holes, which are solutions of $$ \mathcal{N} $$ N = 2 gauged supergravity with vector- and hyper-multiplets. Uplifting the near horizon solutions to D = 11 supergravity on seven-dimensional Sasaki-Einstein manifolds, we show that dyonic AdS4 black holes correspond to AdS2 solutions with electric and magnetic baryonic fluxes in D = 11 supergravity. We identify the off-shell AdS4 black hole solutions with parameters of D = 11 AdS2 solutions without imposing the equations of motion. We calculate the entropy of dyonic black holes, carefully analyzing the Page charge quantization conditions.
We revisit the stringy construction of four-dimensional de-Sitter solutions using orientifolds O8... more We revisit the stringy construction of four-dimensional de-Sitter solutions using orientifolds O8±, proposed by Córdova et al. (2019) [1]. While the original analysis of the supergravity equations is largely numerical, we obtain semi-analytic solutions by treating the curvature as a perturbative parameter. At each order we verify that the (permissive) boundary conditions at the orientifolds are satisfied. To illustrate the advantage of our result, we calculate the four-dimensional Newton constant as a function of the cosmological constant. We also discuss how the discontinuities at O8− can be accounted for in terms of corrections to the worldvolume action.
Recently it was discovered that twisted superconformal index $$ \mathcal{I} $$ I can be used to u... more Recently it was discovered that twisted superconformal index $$ \mathcal{I} $$ I can be used to understand the Bekenstein-Hawking entropy of magnetically charged black holes in AdS spacetime. In this paper we apply the so-called $$ \mathcal{I} $$ I -extremization procedure to three-dimensional gauge field theories and their geometric dual, focusing in particular on the seven-dimensional Sasaki-Einstein manifold M 1,1,1. We generalize recent studies on relations among toric geometry, variational principles, and black hole entropy to the case of AdS2 × Y 9, where Y 9 is a fibration of toric Sasaki-Einstein manifold M 1,1,1 over a two-dimensional Riemann surface Σ g . The nine-dimensional variational problem is given in terms of an entropy functional. In order to illustrate the computations as explicitly as possible, we consider cases where either only mesonic or baryonic fluxes are turned on. By employing the operator counting method, we calculate the S 3 free energy and the topologic...
We study supergravity BPS equations which correspond to mass-deformation of some representative A... more We study supergravity BPS equations which correspond to mass-deformation of some representative AdS/CFT examples. The field theory of interest are $$ \mathcal{N} $$ N = 4, D = 4 super Yang-Mills, the ABJM model in D = 3, and the Brandhuber-Oz fixed point in D = 5. For these gauge theories the free energy with mass terms for matter multiplets is calculable in large-N limit using supersymmetric localization technique. We suggest a perturbative method to solve the supergravity equations. For the dual of mass-deformed ABJM model we reproduce the known exact solutions. For the mass-deformed Brandhuber-Oz theory our method gives the holographic free energy in analytic form. For $$ \mathcal{N} $$ N = 2* theory our result is in good agreement with the localization result.
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