arXiv subjects

James T. Liu

Publications and source records attributed to James T. Liu.

At least 55 records · Page 3Linked to original sources

arXiv2018

The topologically twisted index of $\mathcal N=4$ super-Yang-Mills on $T^2\times S^2$ and the elliptic genus

We examine the topologically twisted index of $\mathcal N=4$ super-Yang-Mills with gauge group $SU(N)$ on $T^2\times S^2$, and demonstrate that it receives contributions from multiple sectors corresponding to the freely acting orbifolds $T^2/\mathbb Z_m\times\mathbb Z_n$ where $N=mn$. After summing over these sectors, the index can be expressed as the elliptic genus of a two-dimensional $\mathcal N=(0,2)$ theory resulting from Kaluza-Klein reduction on $S^2$. This provides an alternate path to the 'high-temperature' limit of the index, and confirms the connection to the right-moving central charge of the $\mathcal N=(0,2)$ theory.

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arXiv2017

Comments on Higher Rank Wilson Loops in ${\cal N}=2^*$

For ${\cal N}=2^*$ theory with $U(N)$ gauge group we evaluate expectation values of Wilson loops in representations described by a rectangular Young tableau with $n$ rows and $k$ columns. The evaluation reduces to a two-matrix model and we explain, using a combination of numerical and analytical techniques, the general properties of the eigenvalue distributions in various regimes of parameters $(N,λ,n,k)$ where $λ$ is the 't Hooft coupling. In the large $N$ limit we present analytic results for the leading and sub-leading contributions. In the particular cases of only one row or one column we reproduce previously known results for the totally symmetry and totally antisymmetric representations. We also extensively discusss the ${\cal N}=4$ limit of the ${\cal N}=2^*$ theory. While establishing these connections we clarify aspects of various orders of limits and how to relax them; we also find it useful to explicitly address details of the genus expansion. As a result, for the totally symmetric Wilson loop we find new contributions that improve the comparison with the dual holographic computation at one loop order in the appropriate regime.

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arXiv2017

Spatial Anisotropy in Nonrelativistic Holography

We examine holographic theories where Lifshitz symmetry is broken with spatial anisotropy. In particular, we focus on the conditions imposed by the null energy condition, and demonstrate that it is possible to have unusual anisotropic fixed points where a subset of the spatial dimensions have negative scaling exponents. We also construct interpolating solutions between UV and IR fixed points and show that there is essentially no restriction placed on the endpoints of the flow once anisotropic scaling is allowed. As an example, we demonstrate a flow from AdS to AdS with $c_{IR}>c_{UV}$ that is allowed by the null energy condition since it proceeds through an intermediate Lorentz-violating region. Finally, we examine the holographic Green's function in anisotropic Lifshitz spacetimes.

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arXiv2017

One-Loop Holographic Weyl Anomaly in Six Dimensions

We compute $\mathcal O(1)$ corrections to the holographic Weyl anomaly for six-dimensional $\mathcal N=(1,0)$ and $(2,0)$ theories using the functional Schrödinger method that is conjectured to work for supersymmetric theories on Ricci-flat backgrounds. We show that these corrections vanish for long representations of the $\mathcal N=(1,0)$ theory, and we obtain an expression for $δ(c-a)$ for short representations with maximum spin two. We also confirm that the one-loop corrections to the $\mathcal N=(2,0)$ M5-brane theory are equal and opposite to the anomaly for the free tensor multiplet. Finally, we discuss the possibility of extending the results to encompass multiplets with spins greater than two.

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arXiv2017

Toward Microstate Counting Beyond Large N in Localization and the Dual One-loop Quantum Supergravity

The topologically twisted index for ABJM theory with gauge group $U(N)_k \times U(N)_{-k}$ has recently been shown, in the large-$N$ limit, to reproduce the Bekenstein-Hawking entropy of certain magnetically charged asymptotically AdS$_4$ black holes. We numerically study the index beyond the large-$N$ limit and provide evidence that it contains a subleading logarithmic term of the form $-1/2\log N$. On the holographic side, this term naturally arises from a one-loop computation. However, we find that the contribution coming from the near horizon states does not reproduce the field theory answer. We give some possible reasons for this apparent discrepancy.

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arXiv2017

Seeing bulk perturbations in Lifshitz holography

We introduce a perturbation $h_{μν}$ onto a background Lifshitz spacetime and examine some of its consequences. In particular, we consider a radially localized perturbation and compute the resulting holographic Green's function to linearized order. At leading order, the Lifshitz Green's function demonstrates suppression of spectral weight at low frequencies, and this feature allows bulk perturbations in the IR to be partially hidden from local boundary probes.

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arXiv2016

One-loop supergravity on $\mathrm{AdS}_4\times S^7/\mathbb{Z}_k$ and comparison with ABJM theory

The large-$N$ limit of ABJM theory is holographically dual to M-theory on AdS$_4\times S^7/\mathbb{Z}_k$. The 3-sphere partition function has been obtained via localization, and its leading behavior $F_{\text{ABJM}}^{(0)}\sim k^{1/2}N^{3/2}$ is exactly reproduced in the dual theory by tree-level supergravity. We extend this comparison to the sub-leading $\mathcal O(N^0)$ order by computing the one-loop supergravity free energy as a function of $k$ and comparing it with the ABJM result. Curiously, we find that the expressions do not match, with $F_{\text{SUGRA}}^{(1)}\sim k^6$, while $F_{\text{ABJM}}^{(1)}\sim k^2$. This suggests that the low-energy approximation $Z_{\text{M-theory}}=Z_{\text{SUGRA}}$ breaks down at one-loop order.

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arXiv2016

Higher Rank ABJM Wilson Loops from Matrix Models

We compute the vacuum expectation values of $1/6$ supersymmetric Wilson loops in higher dimensional representations of the gauge group in ABJM theory. We present results for the $m$-symmetric and $m$-antisymmetric representations by exploiting standard matrix model techniques. At leading order, in the saddle point approximation, our expressions reproduce holographic results from both D6 and D2 branes corresponding to the antisymmetric and symmetric representations, respectively. We also compute 1/N corrections to the leading saddle point results.

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arXiv2016

Holographic Lifshitz fermions and exponentially suppressed spectral weight

The absence of fixed momentum excitations in a theory with Lifshitz scale invariance gives rise to exponential suppression of spectral weight in the low-frequency limit. In the holographic dual, this suppression arises as a consequence of a tunneling barrier that decouples the horizon from the boundary. We compute the spin-1/2 holographic Green's function and show that the form of the barrier is identical to that of the scalar case. We furthermore demonstrate that the suppression factor is universal in the $\hatω\to0$ limit where $\hatω=ω/|\vec k|^z$. In particular, it depends only on $\hatω$ and the critical exponent $z$, and is independent of scaling dimension and spin.

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arXiv2016

Rigid Supersymmetric Backgrounds of 3-dimensional Newton-Cartan Supergravity

Recently, a non-relativistic off-shell formulation of three dimensional Newton-Cartan supergravity was proposed as the $c \rightarrow \infty$ limit of three dimensional $\mathcal{N}=2$ supergravity in arXiv:1505.02095. In the present paper we study supersymmetric backgrounds within this theory. Using integrability constraints for the non-relativistic Killing spinor equations, we explicitly construct all maximally supersymmetric solutions, which admit four supercharges. In addition to these solutions, there are $\frac{1}{2}$-BPS solutions with reduced supersymmetry. We give explicit examples of such backgrounds and derive necessary conditions for backgrounds preserving two supercharges. Finally, we address how supersymmetric backgrounds of $\mathcal{N}=2$ supergravity are connected to the solutions found here in the $c \rightarrow \infty$ limit.

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arXiv2016

Universal features of Lifshitz Green's functions from holography

We examine the behavior of the retarded Green's function in theories with Lifshitz scaling symmetry, both through dual gravitational models and a direct field theory approach. In contrast with the case of a relativistic CFT, where the Green's function is fixed (up to normalization) by symmetry, the generic Lifshitz Green's function can a priori depend on an arbitrary function $\mathcal G(\hatω)$, where $\hatω=ω/|\vec k|^z$ is the scale-invariant ratio of frequency to wavenumber, with dynamical exponent $z$. Nevertheless, we demonstrate that the imaginary part of the retarded Green's function (i.e. the spectral function) of scalar operators is exponentially suppressed in a window of frequencies near zero. This behavior is universal in all Lifshitz theories without additional constraining symmetries. On the gravity side, this result is robust against higher derivative corrections, while on the field theory side we present two $z=2$ examples where the exponential suppression arises from summing the perturbative expansion to infinite order.

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arXiv2015

One-loop Structure of Higher Rank Wilson Loops in AdS/CFT

The half-supersymmetric Wilson loop in $\mathcal N=4$ SYM is arguably the central non-local operator in the AdS/CFT correspondence. On the field theory side, the vacuum expectation values of Wilson loops in arbitrary representations of $SU(N)$ are captured to all orders in perturbation theory by a Gaussian matrix model. Of prominent interest are the $k$-symmetric and $k$-antisymmetric representations, whose gravitational description is given in terms of D3- and D5-branes, respectively, with fluxes in their world volumes. At leading order in $N$ and $λ$ the agreement in both cases is exact. In this note we explore the structure of the next-to-leading order correction in the matrix model and compare with existing string theory calculations. We find agreement in the functional dependence on $k$ but a mismatch in the numerical coefficients.

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arXiv2015

A Holographic c-Theorem for Schrodinger Spacetimes

We prove a c-theorem for holographic renormalization group flows in a Schrodinger spacetime that demonstrates that the effective radius L(r) monotonically decreases from the UV to the IR, where r is the bulk radial coordinate. This result assumes that the bulk matter satisfies the null energy condition, but holds regardless of the value of the critical exponent z. We also construct several numerical examples in a model where the Schrodinger background is realized by a massive vector coupled to a real scalar. The full Schrodinger group is realized when z=2, and in this case it is possible to construct solutions with constant effective z(r)=2 along the entire flow.

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arXiv2015

$c-a$ from the $N=1$ superconformal index

We present a prescription for obtaining the difference of the central charges, c-a, of a four dimensional superconformal quantum field theory from its single-trace index. The formula is derived from a one-loop holographic computation, but is expected to be valid independent of holography. We demonstrate the prescription with several holographic and non-holographic examples. As an application of our formula, we show the AdS/CFT matching of c-a for arbitrary toric quiver CFTs without adjoint matter that are dual to smooth Sasaki-Einstein 5-manifolds.

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arXiv2015

High-Temperature Expansion of Supersymmetric Partition Functions

Di Pietro and Komargodski have recently demonstrated a four-dimensional counterpart of Cardy's formula, which gives the leading high-temperature ($β\rightarrow{0}$) behavior of supersymmetric partition functions $Z^{SUSY}(β)$. Focusing on superconformal theories, we elaborate on the subleading contributions to their formula when applied to free chiral and U(1) vector multiplets. In particular, we see that the high-temperature expansion of $\ln Z^{SUSY}(β)$ terminates at order $β^0$. We also demonstrate how their formula must be modified when applied to SU($N$) toric quiver gauge theories in the planar ($N\rightarrow\infty$) limit. Our method for regularizing the one-loop determinants of chiral and vector multiplets helps to clarify the relation between the 4d $\mathcal{N} = 1$ superconformal index and its corresponding supersymmetric partition function obtained by path-integration.

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arXiv2015

On N=1 partition functions without R-symmetry

We examine the dependence of four-dimensional Euclidean $\mathcal{N}=1$ partition functions on coupling constants. In particular, we focus on backgrounds without R-symmetry, which arise in the rigid limit of old minimal supergravity. Backgrounds preserving a single supercharge may be classified as having either trivial or SU(2) structure, with the former including $S^{4}$. We show that, in the absence of additional symmetries, the partition function depends non-trivially on all couplings in the trivial structure case, and (anti)-holomorphically on couplings in the SU(2) structure case. In both cases, this allows for ambiguities in the form of finite counterterms, which in principle render the partition function unphysical. However, we argue that on dimensional grounds, ambiguities are restricted to finite powers in relevant couplings, and can therefore be kept under control. On the other hand, for backgrounds preserving supercharges of opposite chiralities, the partition function is completely independent of all couplings. In this case, the background admits an R-symmetry, and the partition function is physical, in agreement with the results obtained in the rigid limit of new minimal supergravity. Based on a systematic analysis of supersymmetric invariants, we also demonstrate that $\mathcal{N}=1$ localization is not possible for backgrounds without R-symmetry.

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arXiv2015

Central charges from the $\mathcal{N} = 1$ superconformal index

We present prescriptions for obtaining the central charges, $a$ and $c$, of a four dimensional superconformal quantum field theory from the superconformal index. At infinite $N$, for holographic theories dual to Sasaki-Einstein 5-manifolds the prescriptions give the $\mathcal{O}(1)$ parts of the central charges. This allows us, among other things, to show the exact AdS/CFT matching of $a$ and $c$ for arbitrary toric quiver CFTs without adjoint matter that are dual to smooth Sasaki-Einstein 5-manifolds. In addition, we include evidence from non-holographic theories for the applicability of these results outside of a holographic setting and away from the large-$N$ limit.

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arXiv2014

Hidden horizons in non-relativistic AdS/CFT

We study boundary Green's functions for spacetimes with non-relativistic scaling symmetry. For this class of backgrounds, scalar modes with large transverse momentum, or equivalently low frequency, have an exponentially suppressed imprint on the boundary. We investigate the effect of these modes on holographic two-point functions. We find that the boundary Green's function is generically insensitive to horizon features on small transverse length scales. We explicitly demonstrate this insensitivity for Lifshitz z=2, and then use the WKB approximation to generalize our findings to Lifshitz z>1 and RG flows with a Lifshitz-like region. We also comment on the analogous situation in Schroedinger spacetimes. Finally, we exhibit the analytic properties of the Green's function in these spacetimes.

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