arXiv subjects

Krzysztof Pilch

Publications and source records attributed to Krzysztof Pilch.

At least 19 recordsLinked to original sources

arXiv2021

From Binary Error Correcting Codes to a Relation Between Maximal D=4 and D=3 Supergravities

This short note provides (TensorFlow-based) numerical evidence for the embedability (in the limit of a scalar parameter going to infinity) of the scalar potential of dyonic N=8, D=4 SO(8) supergravity into the scalar potential of N=16, D=3 SO(8)xSO(8) supergravity. One finds that the dyonic $ω$-angle gets identified with the compact U(1) part of the SL(2) factor of the SL(2)xE7(7) subgroup of E8(8).

hep-th↗

arXiv2021

Separability in Consistent Truncations

The separability of the Hamilton-Jacobi equation has a well-known connection to the existence of Killing vectors and rank-two Killing tensors. This paper combines this connection with the detailed knowledge of the compactification metrics of consistent truncations on spheres. The fact that both the inverse metric of such compactifications, as well as the rank-two Killing tensors can be written in terms of bilinears of Killing vectors on the underlying "round metric," enables us to perform a detailed analyses of the separability of the Hamilton-Jacobi equation for consistent truncations. We introduce the idea of a separating isometry and show that when a consistent truncation, without reduction gauge vectors, has such an isometry, then the Hamilton-Jacobi equation is always separable. When gauge vectors are present, the gauge group is required to be an abelian subgroup of the separating isometry to not impede separability. We classify the separating isometries for consistent truncations on spheres, $S^n$, for $n=2, \dots, 7$, and exhibit all the corresponding Killing tensors. These results may be of practical use in both identifying when supergravity solutions belong to consistent truncations and generating separable solutions amenable to scalar probe calculations. Finally, while our primary focus is the Hamilton-Jacobi equation, we also make some remarks about separability of the wave equation.

hep-th↗

arXiv2020

New AdS$_4$ Vacua in Dyonic ISO(7) Gauged Supergravity

We identify 219 AdS$_4$ solutions in four-dimensional dyonically gauged ISO(7) $\mathcal{N}=8$ supergravity and present some of their properties. One of the new solutions preserves $\mathcal{N}=1$ supersymmetry and provides a rare explicit example of an AdS$_4$ vacuum dual to a 3d SCFT with no continuous global symmetry. There are also two new non-supersymmetric solutions for which all 70 scalar fields in the supergravity theory have masses above the BF bound. All of these AdS$_4$ solutions can be uplifted to massive type IIA supergravity. Motivated by this we present the low lying operator spectra of the dual 3d CFTs for all known supersymmetric AdS$_4$ solutions in the theory and organize them into superconformal multiplets.

hep-th↗

arXiv2020

Brane-Jet Instabilities

With one exception, all known non-supersymmetric AdS$_4$ and AdS$_5$ vacua of gauged maximal supergravities that descend from string and M theory have been shown to have modes with mass below the BF bound. The remaining non-supersymmetric AdS solution is perturbatively stable within gauged maximal supergravity, and hence appears to contradict recent conjectures about the AdS stability based on the weak gravity conjecture. We show that this solution is actually unstable by exhibiting a new decay channel, which is only visible when the solution is uplifted to eleven dimensions. In particular, M2 brane probes at generic locations inside the internal manifold are attracted to the Poincaré horizon, only to be expelled as "brane jets" along certain directions of the internal manifold. Such instabilities can arise in any non-supersymmetric AdS vacuum in any dimension. When a brane-jet instability is present, the force that expels the branes is the same as the force felt by a probe brane whose mass is less than its charge.

hep-th↗

arXiv2020

A Cornucopia of AdS$_5$ Vacua

We report on a systematic search for AdS$_5$ vacua corresponding to critical points of the potential in the five-dimensional $\mathcal{N}=8$ SO(6) gauged supergravity. By employing Google's TensorFlow Machine Learning library, we find the total of 32 critical points including 5 previously known ones. All 27 new critical points are non-supersymmetric. We compute the mass spectra of scalar fluctuatons for all points and find that the non-supersymmetric AdS$_5$ vacua are perturbatively unstable. Many of the new critical points can be found analytically within consistent truncations of the $\mathcal{N}=8$ supergravity with respect to discrete subgroups of the S(O(6)$\times$ GL(2,$\mathbb{R}$)) symmetry of the potential. In particular, we discuss in detail a $\mathbb{Z}_2^3$-invariant truncation with 10 scalar fields and 15 critical points. We also compute explicitly the scalar potential in a $\mathbb{Z}_2^2$-invariant extension of that truncation to 18 scalar fields and reproduce 17 of the 32 critical points from the numerical search. Finally, we show that the full potential as a function of 42 scalar fields can be studied analytically using the so-called solvable parametrization. In particular, we find that all critical points lie in a $\mathbb{Z}_2$-invariant subspace spanned by 22 scalar fields.

hep-th↗

arXiv2020

Holographic Interfaces in N=4 SYM: Janus and J-folds

We find the holographic dual to the three classes of superconformal Janus interfaces in $\mathcal{N}=4$ SYM that preserve three-dimensional $\mathcal{N}=4$, $\mathcal{N}=2$, and $\mathcal{N}=1$ supersymmetry. The solutions are constructed in five-dimensional SO(6) maximal gauged supergravity and are then uplifted to type IIB supergravity. Corresponding to each of the three classes of Janus solutions, there are also AdS$_4\times S^1\times S^5$ J-fold backgrounds. These J-folds have a non-trivial SL$(2,\mathbb{Z})$ monodromy for the axio-dilaton on the $S^1$ and are dual to three-dimensional superconformal field theories.

hep-th↗

arXiv2019

A new N=1 AdS4 Vacuum of Maximal Supergravity

The recent comprehensive numerical study of critical points of the scalar potential of four-dimensional N=8, SO(8) gauged supergravity using Machine Learning software has led to a discovery of a new N=1 vacuum with a triality-invariant SO(3) symmetry. Guided by the numerical data for that point, we obtain a consistent SO(3)xZ2-invariant truncation of the N=8 theory to an N=1 supergravity with three chiral multiplets. Critical points of the truncated scalar potential include both the N=1 point as well as two new non-supersymmetric and perturbatively unstable points not found by previous searches. Studying the structure of the submanifold of SO(3)xZ2-invariant supergravity scalars, we find that it has a simple interpretation as a submanifold of the 14-dimensional Z2^3-invariant scalar manifold (SU(1,1)/U(1))^7, for which we find a rather remarkable superpotential whose structure matches the single bit error correcting (7, 4) Hamming code. This 14-dimensional scalar manifold contains approximately one quarter of the known critical points. We also show that there exists a smooth supersymmetric domain wall which interpolates between the new N=1 AdS4 solution and the maximally supersymmetric AdS4 vacuum. Using holography, this result indicates the existence of an N=1 RG flow from the ABJM SCFT to a new strongly interacting conformal fixed point in the IR.

hep-th↗

arXiv2019

Janus and J-fold Solutions from Sasaki-Einstein Manifolds

We show that for every Sasaki-Einstein manifold, $M_5$, the AdS$_5\times M_5$ background of type IIB supergravity admits two universal deformations leading to supersymmetric AdS$_4$ solutions. One class of solutions describes an AdS$_4$ domain wall in AdS$_5$ and is dual to a Janus configuration with $\mathcal{N}=1$ supersymmetry. The other class of backgrounds is of the form AdS$_4\times S^1\times M_5$ with a non-trivial SL$(2,\mathbb{Z})$ monodromy for the IIB axio-dilaton along the $S^1$. These AdS$_4$ solutions are dual to three-dimensional $\mathcal{N}=1$ SCFTs. Using holography we express the $S^3$ free energy of these theories in terms of the conformal anomaly of the four-dimensional $\mathcal{N}=1$ SCFT arising from D3-branes on the Calabi-Yau cone over $M_5$.

hep-th↗

arXiv2018

Mass Deformations of the ABJM Theory: The Holographic Free Energy

We find a class of new supersymmetric Euclidean solutions in four-dimensional maximal gauged supergravity. The holographic dual description of these backgrounds is given by a mass-deformation of the ABJM theory with general values for the R-charges. We calculate the $S^3$ free energy for the supergravity backgrounds and find agreement with the supersymmetric localization calculation of the free energy in the large $N$ limit.

hep-th↗

arXiv2018

Mass-deformed ABJM and Black Holes in AdS$_4$

We find a class of new supersymmetric dyonic black holes in four-dimensional maximal gauged supergravity which are asymptotic to the ${\rm SU(3)}\times {\rm U(1)}$ invariant AdS$_4$ Warner vacuum. These black holes can be embedded in eleven-dimensional supergravity where they describe the backreaction of M2-branes wrapped on a Riemann surface. The holographic dual description of these supergravity backgrounds is given by a partial topological twist on a Riemann surface of a three-dimensional $\mathcal{N}=2$ SCFT that is obtained by a mass-deformation of the ABJM theory. We compute explicitly the topologically twisted index of this SCFT and show that it accounts for the entropy of the black holes.

hep-th↗

arXiv2016

Boundary Terms and Three-Point Functions: An AdS/CFT Puzzle Resolved

${\cal N} = 8$ superconformal field theories, such as the ABJM theory at Chern-Simons level $k=1$ or $2$, contain 35 scalar operators ${\cal O}_{IJ}$ with $Δ=1$ in the ${\bf 35}_v$ representation of SO(8). The 3-point correlation function of these operators is non-vanishing, and indeed can be calculated non-perturbatively in the field theory. But its AdS$_4$ gravity dual, obtained from gauged ${\cal N}=8$ supergravity, has no cubic $A^3$ couplings in its Lagrangian, where $A^{IJ}$ is the bulk dual of ${\cal O}_{IJ}$. So conventional Witten diagrams cannot furnish the field theory result. We show that the extension of bulk supersymmetry to the AdS$_4$ boundary requires the introduction of a finite $A^3$ counterterm that does provide a perfect match to the 3-point correlator. Boundary supersymmetry also requires infinite counterterms which agree with the method of holographic renormalization. The generating functional of correlation functions of the $Δ=1$ operators is the Legendre transform of the on-shell action, and the supersymmetry properties of this functional play a significant role in our treatment.

hep-th↗

arXiv2015

$\mathcal{N}=2$ Supersymmetric Janus Solutions and Flows: From Gauged Supergravity to M Theory

We investigate a family of SU(3)$\times$U(1)$\times$U(1)-invariant holographic flows and Janus solutions obtained from gauged $\mathcal{N}=8$ supergravity in four dimensions. We give complete details of how to use the uplift formulae to obtain the corresponding solutions in M theory. While the flow solutions appear to be singular from the four-dimensional perspective, we find that the eleven-dimensional solutions are much better behaved and give rise to interesting new classes of compactification geometries that are smooth, up to orbifolds, in the infra-red limit. Our solutions involve new phases in which M2 branes polarize partially or even completely into M5 branes. We derive the eleven-dimensional supersymmetries and show that the eleven-dimensional equations of motion and BPS equations are indeed satisfied as a consequence of their four-dimensional counterparts. Apart from elucidating a whole new class of eleven-dimensional Janus and flow solutions, our work provides extensive and highly non-trivial tests of the recently-derived uplift formulae.

hep-th↗

arXiv2015

Flowing to Higher Dimensions: A New Strongly-Coupled Phase on M2 Branes

We describe a one-parameter family of new holographic RG flows that start from $AdS_4 \times S^7$ and go to $\widehat{AdS_5} \times {\cal B}_6$, where ${\cal B}_6$ is conformal to a Kähler manifold and $\widehat{AdS_5}$ is Poincaré $AdS_5$ with one spatial direction compactified and fibered over ${\cal B}_6$. The new solutions "flow up dimensions," going from the $(2+1)$-dimensional conformal field theory on M2 branes in the UV to a $(3+1)$-dimensional field theory on intersecting M5 branes in the infra-red. The M2 branes completely polarize into M5 branes along the flow and the Poincaré sections of the $\widehat{AdS_5}$ are the $(3+1)$-dimensional common intersection of the M5 branes. The emergence of the extra dimension in the infra-red suggests a new strongly-coupled phase of the M2 brane and ABJM theories in which charged solitons are becoming massless. The flow solution is first analyzed by finding a four-dimensional $N \! = \! 2$ supersymmetric flow in $N \! = \! 8$ gauged supergravity. This is then generalized to a one parameter family of non-supersymmetric flows. The infra-red limit of the solutions appears to be quite singular in four dimensions but the uplift to eleven-dimensional supergravity is remarkable and regular (up to orbifolding). Our construction is a non-trivial application of the recently derived uplift formulae for fluxes, going well beyond the earlier constructions of stationary points solutions. The eleven-dimensional supersymmetry is also analyzed and shows how, for the supersymmetric flow, the M2-brane supersymmetry in the UV is polarized entirely into M5-brane supersymmetry in the infra-red.

hep-th↗

arXiv2015

An SO(3)$\times$SO(3) invariant solution of $D=11$ supergravity

We construct a new SO(3)$\times$SO(3) invariant non-supersymmetric solution of the bosonic field equations of $D=11$ supergravity from the corresponding stationary point of maximal gauged $N=8$ supergravity by making use of the non-linear uplift formulae for the metric and the 3-form potential. The latter are crucial as this solution appears to be inaccessible to traditional techniques of solving Einstein's field equations, and is arguably the most complicated closed form solution of this type ever found. The solution is also a promising candidate for a stable non-supersymmetric solution of M-theory uplifted from gauged supergravity. The technique that we present here may be applied more generally to uplift other solutions of gauged supergravity.

hep-th↗

arXiv2014

(0,2) SCFTs from the Leigh-Strassler Fixed Point

We show that there is a family of two-dimensional $(0,2)$ SCFTs associated with twisted compactifications of the four-dimensional $\mathcal{N}=1$ Leigh-Strassler fixed point on a closed hyperbolic Riemann surface. We calculate the central charges for this class of theories using anomalies and $c$-extremization. In a suitable truncation of the five-dimensional maximal supergravity, we construct supersymmetric $AdS_3$ solutions that are holographic duals of those two-dimensional $(0,2)$ SCFTs. We also exhibit supersymmetric domain wall solutions that are holographically dual to the RG flows between the four-dimensional and two-dimensional theories.

hep-th↗

arXiv2013

Supersymmetric Janus Solutions in Four Dimensions

We use maximal gauged supergravity in four dimensions to construct the gravity dual of a class of supersymmetric conformal interfaces in the theory on the world-volume of multiple M2-branes. We study three classes of examples in which the $(1+1)$-dimensional defects preserve $(4,4)$, $(0,2)$ or $(0,1)$ supersymmetry. Many of the solutions have the maximally supersymmetric $AdS_4$ vacuum dual to the $\mathcal{N}=8$ ABJM theory on both sides of the interface. We also find new special classes of solutions including one that interpolates between the maximally supersymmetric vacuum and a conformal fixed point with $\mathcal{N}=1$ supersymmetry and $G_2$ global symmetry. We find another solution that interpolates between two distinct conformal fixed points with $\mathcal{N}=1$ supersymmetry and $G_2$ global symmetry. In eleven dimensions, this $G_2$ to $G_2$ solution corresponds to a domain wall across which a magnetic flux reverses orientation.

hep-th↗

arXiv2013

On perturbative instability of Pope-Warner solutions on Sasaki-Einstein manifolds

Given a Sasaki-Einstein manifold, M_7, there is the N=2 supersymmetric AdS_4 x M_7 Freund-Rubin solution of eleven-dimensional supergravity and the corresponding non-supersymmetric solutions: the perturbatively stable skew-whiffed solution, the perturbatively unstable Englert solution, and the Pope-Warner solution, which is known to be perturbatively unstable when M_7 is the seven-sphere or, more generally, a tri-Sasakian manifold. We show that similar perturbative instability of the Pope-Warner solution will arise for any Sasaki-Einstein manifold, M_7, admitting a basic, primitive, transverse (1,1)-eigenform of the Hodge-de Rham Laplacian with the eigenvalue in the range between 2(9-4\sqrt 3) and 2(9+4\sqrt 3). Existence of such (1,1)-forms on all homogeneous Sasaki-Einstein manifolds can be shown explicitly using the Kahler quotient construction or the standard harmonic expansion. The latter shows that the instability arises from the coupling between the Pope-Warner background and Kaluza-Klein scalar modes that at the supersymmetric point lie in a long Z-vector supermultiplet. We also verify that the instability persists for the orbifolds of homogeneous Sasaki-Einstein manifolds that have been discussed recently.

hep-th↗

arXiv2012

On Supersymmetric Flux Solutions of M-theory

Motivated by the geometric structures of supersymmetric holographic RG-flows, we scan for N=2 AdS_4 solutions in M-theory. One particularly well understood holographic RG flow in M-theory is dual to a mass deformation of the N=8 Chern-Simons theory. We utilize an Ansatz which is a natural generalization of this background in our scan. We find a single new solution with non-trivial internal flux and the topology of S^7. Interestingly, despite our Ansatz being quite general, within our system we rule out solutions with internal flux on more general Sasaki-Einstein seven manifolds.

hep-th↗