arXiv subjects

James T. Liu

Publications and source records attributed to James T. Liu.

At least 37 records · Page 2Linked to original sources

arXiv2021

Sub-leading Structures in Superconformal Indices: Subdominant Saddles and Logarithmic Contributions

We systematically study various sub-leading structures in the superconformal index of ${\cal N}=4$ supersymmetric Yang-Mills theory with SU($N$) gauge group. We concentrate in the superconformal index description as a matrix model of elliptic gamma functions and in the Bethe-Ansatz presentation. Our saddle-point approximation goes beyond the Cardy-like limit and we uncover various saddles governed by a matrix model corresponding to SU($N$) Chern-Simons theory. The dominant saddle, however, leads to perfect agreement with the Bethe-Ansatz approach. We also determine the logarithmic correction to the superconformal index to be $\log N$, finding precise agreement between the saddle-point and Bethe-Ansatz approaches in their respective approximations. We generalize the two approaches to cover a large class of 4d ${\cal N}=1$ superconformal theories. We find that also in this case both approximations agree all the way down to a universal contribution of the form $\log N$. The universality of this last result constitutes a robust signature of this ultraviolet description of asymptotically AdS$_5$ black holes and could be tested by low-energy IIB supergravity.

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arXiv2021

Subleading corrections to the $S^3$ free energy of necklace quiver theories dual to massive IIA

We investigate the $S^3$ free energy of $\mathcal N=3$ Chern-Simons-matter quiver gauge theories with gauge group $U(N)^r~(r\geq2)$ where the sum of Chern-Simons levels does not vanish, beyond the leading order in the large-$N$ expansion. We take two different approaches to explore the sub-leading structures of the free energy. First we evaluate the matrix integral for the partition function in the 't~Hooft limit using a saddle point approximation. Second we use an ideal Fermi-gas model to compute the same partition function, but in the limit of fixed Chern-Simons levels. The resulting expressions for the free energy $F=-\log Z$ are consistent with each other at the leading and first sub-leading order. The Fermi-gas approach also hints at a universal $\frac{1}{6}\log N$ correction to the free energy. Since the quiver gauge theories we consider are dual to massive Type IIA theory, we expect our results to match sub-leading corrections to the holographic dual free energy, which have not yet been fully investigated.

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arXiv2021

Repulsive Black Holes and Higher-Derivatives

In two-derivative theories of gravity coupled to matter, charged black holes are self-attractive at large distances, with the force vanishing at zero temperature. However, in the presence of massless scalar fields and four-derivative corrections, zero-temperature black holes no longer need to obey the no-force condition. In this paper, we show how to calculate the long-range force between such black holes. We develop an efficient method for computing the higher-derivative corrections to the scalar charges when the two-derivative theory has a shift symmetry, and compute the resulting force in a variety of examples. We find that higher-derivative corrected black holes may be self-attractive or self-repulsive, depending on the value of the Wilson coefficients and the VEVs of scalar moduli. Indeed, we find black hole solutions which are both superextremal and self-attractive. Furthermore, we present examples where no choice of higher-derivative coefficients allows for self-repulsive black hole states in all directions in charge space. This suggests that, unlike the Weak Gravity Conjecture, which may be satisfied by the black hole spectrum alone, the Repulsive Force Conjecture requires additional constraints on the spectrum of charged particles.

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arXiv2021

Subleading Corrections in N=3 Gaiotto-Tomasiello Theory

We study subleading corrections to the genus-zero free energy of the $\mathcal{N}=3$ Gaiotto-Tomasiello theory. In general, we obtain the endpoints and free energy as a set of parametric equations via contour integrals of the planar resolvent, up to exponentially suppressed corrections. In the particular case that the two gauge groups in the quiver are of equal rank, we find an explicit (perturbative) expansion for the free energy. If, additionally, both groups have equal levels, then we find the full expression for the genus-zero free energy, modulo exponentially suppressed corrections. We also verify our results numerically.

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arXiv2021

The Bethe-Ansatz approach to the $\mathcal N=4$ superconformal index at finite rank

We investigate the Bethe-Ansatz (BA) approach to the superconformal index of ${\cal N}=4$ supersymmetric Yang-Mills with SU($N$) gauge group in the context of finite rank, $N$. We explicitly explore the role of the various types of solutions to the Bethe-Ansatz Equations (BAE) in recovering the exact index for $N=2,3$. We classify the BAE solutions as standard (corresponding to a freely acting orbifold $T^2/\mathbb{Z}_m \times \mathbb{Z}_n$) and non-standard. For $N=2$, we find that the index is fully recovered by standard solutions and displays an interesting pattern of cancellations. However, for $N\ge 3$, the standard solutions alone do not suffice to reconstruct the index. We present quantitative arguments in various regimes of fugacities that highlight the challenging role played by the continuous families of non-standard solutions.

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arXiv2021

A NUT Charge Weak Gravity Conjecture from Dimensional Reduction

We analyze the constraints on four-derivative corrections to 5d Einstein-Maxwell theory from the black hole Weak Gravity Conjecture (WGC). We calculate the leading corrections to the extremal mass of asymptotically flat 5d charged solutions as well as 4d Kaluza-Klein compactifications. The WGC bounds from the latter, interpreted as 4d dyonic black holes, are found to be strictly stronger. As magnetic graviphoton charge lifts to a NUT-like charge in 5d, we argue that the logic of the WGC should apply to these topological charges as well and leads to new constraints on purely gravitational theories.

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arXiv2021

Higher-derivative couplings in string theory: five-point contact terms

We compute the tree-level $H^2R^3$ couplings of type II strings and provide some basic tests of the couplings by considering both K3 and Calabi-Yau threefold compactifications. Curiously, additional kinematical structures show up at tree level that are not present in the one-loop couplings. This has interesting implications for type II supersymmetry as well as $SL(2, \mathbb Z)$ duality in type IIB strings.

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arXiv2021

Asymptotic growth of the 4d $\mathcal N=4$ index and partially deconfined phases

We study the Cardy-like asymptotics of the 4d $\mathcal N=4$ index and demonstrate the existence of partially deconfined phases where the asymptotic growth of the index is not as rapid as in the fully deconfined case. We then take the large-$N$ limit after the Cardy-like limit and make a conjecture for the leading asymptotics of the index. While the Cardy-like behavior is derived using the integral representation of the index, we demonstrate how the same results can be obtained using the Bethe ansatz type approach as well. In doing so, we discover new non-standard solutions to the elliptic Bethe ansatz equations including continuous families of solutions for $SU(N)$ theory with $N\ge3$. We argue that the existence of both standard and continuous non-standard solutions has a natural interpretation in terms of vacua of $\mathcal N=1^*$ theory on $\mathbb R^3\times S^1$.

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arXiv2020

The large-N partition function for non-parity-invariant Chern-Simons-matter theories

We extend the Fermi gas approach to a class of ABJM-like necklace quiver theories without parity invariance. The resulting partition function on $S^3$ retains the form of an Airy function, but now includes a phase that scales as $Nk$ in the large-$N$ limit where $k$ is an overall Chern-Simons level. We demonstrate the presence of this phase both analytically and numerically in the case of a three node quiver.

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arXiv2020

Higher-Derivative Corrections to Entropy and the Weak Gravity Conjecture in Anti-de Sitter Space

We compute the four-derivative corrections to the geometry, extremality bound, and thermodynamic quantities of AdS-Reissner-Nordstr{ö}m black holes for general dimensions and horizon geometries. We confirm the universal relationship between the extremality shift at fixed charge and the shift of the microcanonical entropy, and discuss the consequences of this relation for the Weak Gravity Conjecture in AdS. The thermodynamic corrections are calculated using two different methods: first by explicitly solving the higher-derivative equations of motion and second, by evaluating the higher-derivative Euclidean on-shell action on the leading-order solution. In both cases we find agreement, up to the addition of a Casimir energy in odd dimensions. We derive the bounds on the four-derivative Wilson coefficients implied by the conjectured positivity of the leading corrections to the microcanonical entropy of thermodynamically stable black holes. These include the requirement that the coefficient of Riemann-squared is positive, meaning that the positivity of the entropy shift is related to the condition that $c - a$ is positive in the dual CFT. We discuss implications for the deviation of $η/s$ from its universal value and a potential lower bound.

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arXiv2020

Subleading corrections to the free energy in a theory with $N^{5/3}$ scaling

We numerically investigate the sphere partition function of a Chern-Simons-matter theory with $SU(N)$ gauge group at level $k$ coupled to three adjoint chiral multiplets that is dual to massive IIA theory. Beyond the leading order $N^{5/3}$ behavior of the free energy, we find numerical evidence for a term of the form $(2/9)\log N-(1/18)\log k$. We conjecture that the $(2/9)\log N$ term may be universal in theories with $N^{5/3}$ scaling in the large-$N$ limit with the Chern-Simons level $k$ held fixed.

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arXiv2019

The Scales of Black Holes with nAdS$_2$ Geometry

We study nearly extreme black holes with nearly AdS$_2$ horizon geometry in various settings inspired by string theory. Our focus is on the scales of the nAdS$_2$ region and their relation to microscopic theory. These scales are determined by a generalization of the attractor mechanism for extremal black holes and realized geometrically as the normal derivatives along the extremal attractor flow. In some cases the scales are equivalently determined by the charge dependence of the extremal attractor by itself. Our examples include near extreme black holes in $D\geq 4$ dimensions, AdS boundary conditions, rotation, and 5D black holes on the non-BPS branch.

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arXiv2019

Subleading Microstate Counting in the Dual to Massive Type IIA

We study the topologically twisted index of a certain Chern-Simons matter theory with $SU(N)$ level $k$ gauge group on a genus $g$ Riemann surface times a circle. For this theory it is known that the logarithm of the topologically twisted index grows as $N^{5/3}$ and that it matches the Bekenstein-Hawking entropy of certain magnetically charged asymptotically $AdS_4\times S^6$ black holes in massive type IIA supergravity. Through a combination of numerical and analytical techniques we study the subleading in $N$ structure. We demonstrate precise analytic cancellation of terms of orders $N\log\,N$ and $N^{1/3}\log N$ and show numerical cancellation for terms of order $N$. As a result, the first subleading correction is of order $N^{2/3}$. Furthermore, we provide evidence for the presence of a term of the form $(g-1)(7/18) \log \,N$ which constitutes a microscopic prediction for the one-loop contribution coming from the massless gravitational degrees of freedom in the massive IIA black hole.

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arXiv2019

Gauged Supergravity from the Lunin-Maldacena background

We show how to expand the Lunin-Maldacena solution to the full bosonic sector of gauged $\mathcal N=2$ supergravity. In particular, we construct a consistent truncation of IIB supergravity on a $β$-deformed $\mathrm{AdS}_5\times S^5$ background retaining a dynamical metric and graviphoton in five dimensions. We comment on the relation between this solution and similar constructions on Sasaki-Einstein manifolds, as well as the possibility of further consistent truncations which generalize the Lunin-Maldacena solution.

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arXiv2019

Quantum Corrections to Central Charges and Supersymmetric Casimir Energy in AdS$_3$/CFT$_2$

We study the Casimir energy of bulk fields in AdS$_3$ and its relation to subleading terms in the central charge of the dual CFT$_2$. Computing both sides of the standard CFT$_2$ relation $E=-c/12$ independently we show that this relation is not necessarily satisfied at the level of individual bulk supergravity states, but in theories with sufficient supersymmetry it is restored at the level of bulk supermultiplets. Assuming only $(0,2)$ supersymmetry (or more), we improve the situation by relating quantum corrections to the central charge and the supersymmetric Casimir energy which in turn is related to an index. These relations adapt recent progress on the AdS$_5$/CFT$_4$ correspondence to AdS$_3$/CFT$_2$ holography. We test our formula successfully in several examples, including the $(0,4)$ MSW theory describing classes of 4D black holes and the large $(4,4)$ theory that is interesting for higher spin holography. We also make predictions for the subleading central charges in several recently proposed $(2,2)$ dualities where the CFT$_2$ is not yet well-understood.

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arXiv2019

The Weyl Anomaly from the 6D Superconformal Index

We explore the connection between the holographic Weyl anomaly and the superconformal index in six-dimensional $(1,0)$ theories. Using earlier results from holographic computations of the $\mathcal O(1)$ contributions $δa$ and $δ(c-a)$ to the corresponding six-dimensional Weyl anomaly coefficients, we derive a pair of differential operators that extracts these values from the large-$N$ single-trace index. In doing so, we also highlight the structure of these corrections in terms of group theory invariants of the superconformal representations.

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arXiv2018

Gauged Six-Dimensional Supergravity from Warped IIB Reductions

We find a family of complete non-linear Kaluza-Kein reduction ansatze from type IIB supergravity to Romans' 6D $F(4)$ gauged supergravity in the bosonic sector. The reduction is over a sphere $S^2$ and a Riemann surface $Σ$, and depends on a pair of arbitrary locally holomorphic functions $\mathcal{A}_{\pm}$ on $Σ$. This family of reductions is inspired by the recent construction of 1/2 BPS supersymmetric warped $AdS_6$ solutions of IIB supergravity that depend on these same functions $\mathcal{A}_{\pm}$.

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arXiv2018

A One-loop Test of Quantum Black Holes in Anti de Sitter Space

Within eleven dimensional supergravity we compute the logarithmic correction to the entropy of magnetically charged asymptotically AdS${}_4$ black holes with arbitrary horizon topology. We find perfect agreement with the expected microscopic result arising from the dual field theory computation of the topologically twisted index. Our result relies crucially on a particular limit to the extremal black hole case and clarifies some aspects of quantum corrections in asymptotically AdS spacetimes.

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