Search

The revival mechanism in dormant bacteria is a puzzling and open issue. We propose a model of information diffusion on a regular grid where agents represent bacteria and their mutual interactions implement quorum sensing. Agents may have different metabolic characteristics corresponding to multiple phenotypes. The intra/inter phenotype cooperation is analyzed under different metabolic and productivity conditions. We study the interactions between rapidly reproducing active bacteria and non-reproducing quiescent bacteria. We highlight the conditions under which the quiescent bacteria may revive. The occurrence of revival is generally related to a change in environmental conditions. Our results support this picture showing that revival can be mediated by the presence of different catalyst bacteria that produce the necessary resources ., Comment: 5 figures, 18 pages

As was shown in arXiv:2303.15207, the leading large $N$, fixed $k$ correction in the localization result for the expectation value of the $\frac{1}{2}$-BPS circular Wilson loop in $U(N)_{k}\times U(N)_{-k}$ ABJM theory given by the $(\sin\frac{2\pi}{ k})^{-1}$ factor can be reproduced on the dual M-theory side as the one-loop correction in the partition function of an M2 brane in AdS$_{4}\times S^{7}/\mathbb{Z}_{k}$ with AdS$_{2}\times S^{1}$ world volume. Here we prove, following the suggestion in arXiv:2408.10070, that the analogous fact is true also for the corresponding correction $B_1=-\frac{1}{2\pi k}\cot\frac{2\pi}{k}$ in the localization result for the Bremsstrahlung function associated with the Wilson line with a small cusp in either AdS$_4$ or $\rm CP^3$. The corresponding M2 brane is wrapped on the 11d circle and generalizes the type IIA string solution in AdS$_{4}\times \rm CP^3$ ending on the cusped line. We show that the one-loop term in the M2 brane partition function reproduces the localization expression for $B_1$ as the coefficient of the leading term in its small cusp expansion., Comment: 29 pages. v2: typos fixed

We consider two supersymmetric M5 brane probe solutions in $\textrm{AdS}_7 \times S^4$ and one in $\textrm{AdS}_4 \times S^7$ that all have the $\textrm{AdS}_3 \times S^3$ world-volume geometry. The values of the classical action of the first two M5 probes (with $S^3$ in $\textrm{AdS}_7$ or in $S^4$) are related to the leading $N^2$ parts in the anomaly b-coefficient in the (2,0) theory corresponding to a spherical surface defect in symmetric or antisymmetric $SU(N)$ representations. We present a detailed computation of the corresponding one-loop M5 brane partition functions finding that they vanish (in a particular regularization). This implies the vanishing of the order $N^0$ part in the b-anomaly coefficients, in agreement with earlier predictions for their exact values. It remains, however, a puzzle of how to reproduce the non-vanishing order $N$ terms in these coefficients within the semiclassical M5-brane probe setup., Comment: 48 pages. v3: minor changes

The giant graviton expansion of the line defect Schur index in four dimensional $\mathcal N=4$ $U(N)$ SYM was recently proposed in arXiv:2403.11543 to be captured in the dual string theory by counting fluctuations states of two half-infinite fundamental strings in $AdS_{5}\times S^{5}$ ending on the line defect and D3 brane giant. However, agreement with the gauge theory data for the defect line index at finite $N$ required the inclusion of ad hoc extra contributions with unclear origin. We discuss the large $N$ leading order contribution of the giant graviton expansion of the defect line index by a direct analysis of semiclassical string partition function in a twisted background. We discuss supersymmetric boundary conditions in the presence of the D3 brane and evaluate the quadratic fluctuations effective action by introducing a suitable projection of fluctuation modes. We show that the extra contributions to the single giant graviton correction found in arXiv:2403.11543 correspond to a supersymmetric Casimir energy contribution., Comment: 33 pages

We present a computational scheme for predicting the ligands that bind to a pocket of known structure. It is based on the generation of a general abstract representation of the molecules, which is invariant to rotations, translations and permutations of atoms, and has some degree of isometry with the space of conformations. We use these representations to train a non-deep machine learning algorithm to classify the binding between pockets and molecule pairs, and show that this approach has a better generalization capability than existing methods.

We consider 4d $\mathcal N=4$ $U(N)$ SYM and the leading giant graviton correction to the Schur defect 2-point functions of $\frac{1}{2}$-BPS Wilson lines in rank-$k$ symmetric and antisymmetric representations. We study in particular the large $k$ limit for the symmetric case and the regime $1\ll k \ll N$ in the antisymmetric one. We present exact results for the correction in agreement with matrix model evaluation at finite $N,k$. The Wilson lines in symmetric/antisymmetric representations admit a description in terms of D3$_{k}$ and D5$_{k}$ brane probes representing a collection of $k$ fundamental strings. In this picture, giant graviton corrections come from fluctuations of brane probes in presence of a wrapped D3 brane giant graviton. In particular, for the antisymmetric case, our leading correction matches the half-index of the 3d $\mathcal N=4$ Maxwell theory living on the 3d disk which is a part of the giant graviton divided out by the D5$_{k}$ probe, as recently proposed in arXiv:2404.08302. For the symmetric case at large $k$, we derive an explicit exact residue formula for the leading correction., Comment: 26 pages

We consider Schur line defect correlators in four dimensional $\mathcal N=4$ $U(N)$ SYM and their giant graviton expansion encoding finite $N$ corrections to the large $N$ limit. We compute in closed form the single giant graviton contribution to correlators with general insertions of $\frac{1}{2}$-BPS charged Wilson lines. For the 2-point function with fundamental and anti-fundamental Wilson lines, we match the result from fluctuations of two half-infinite strings ending on the giant graviton, recently proposed in arXiv:2403.11543. In particular, we prove exact factorization of the defect contribution with respect to wrapped D3 brane fluctuations representing the single giant graviton correction to the undecorated Schur index. This follows from a finite-difference representation of the Schur line defect index in terms of the index without defects, and similar factorization holds quite generally for more complicated defect configurations. In particular, the single giant graviton contribution to the 4-point function with two fundamental and two anti-fundamental lines is computed and discussed in this perspective., Comment: 24 pages. v2: minor changes, typos fixed

The flavored superconformal Schur index of $\mathcal N=4$ $U(N)$ SYM has finite $N$ corrections encoded in its giant graviton expansion in terms of D3 branes wrapped in $AdS_{5}\times S^{5}$. The key element of this decomposition is the non-trivial index of the theory living on the wrapped brane system. A remarkable feature of the Schur limit is that the brane index is an analytic continuation of the flavored index of $\mathcal N=4$ $U(n)$ SYM, where $n$ is the total brane wrapping number. We exploit recent exact results about the Schur index of $\mathcal N=4$ $U(N)$ SYM to evaluate the closed form of the the brane indices appearing in the giant graviton expansion. Away from the unflavored limit, they are characterized by quasimodular forms providing exact information at all orders in the index universal fugacity. As an application of these results, we present novel exact expressions for the giant graviton expansion of the unflavored Schur index in a class of four dimensional $\mathcal N=2$ theories with equal central charges $a=c$, i.e. the non-Lagrangian theories $\widehat{\Gamma}(SU(N))$ with $\Gamma = E_{6}, E_{7}, E_{8}$., Comment: 34 pages. v2: minor changes

We consider the refined Schur superconformal index of 4d $\mathcal N=4$ $U(N)$ SYM and the first term of its giant-graviton expansion, first predicted in arXiv:2001.11667 using indirect superconformal algebra considerations and analytic continuation of fugacities. This correction is the leading non-perturbative correction to the index at large $N$ and we reproduce it from the semiclassical partition function of quantum D3 brane wrapped on $S^{1}\times S^{3}$ in a twisted modification of the $AdS_{5}\times S^{5}$ string background, depending on the index R-symmetry fugacity. Our calculation does not exploit directly supersymmetry. It is based on the determination of the partition function of the various bosonic and fermionic fluctuations on the wrapped brane whose action is conformal with specific constant holonomies along thermal cycle. We show how those partition functions may be obtained by adapting the operator counting method of Cardy to the twisted background., Comment: 31 pages

We study four-dimensional $\mathcal N=2$ superconformal circular, cyclic symmetric quiver theories which are planar equivalent to $\mathcal N=4$ super Yang-Mills. We use localization to compute nonplanar corrections to the free energy and the circular half-BPS Wilson loop in these theories for an arbitrary number of nodes, and examine their behaviour in the limit of long quivers. Exploiting the relationship between the localization quiver matrix integrals and an integrable Bessel operator, we find a closed-form expression for the leading nonplanar correction to both observables in the limit when the number of nodes and 't Hooft coupling become large. We demonstrate that it has different asymptotic behaviour depending on how the two parameters are compared, and interpret this behaviour in terms of properties of a lattice model defined on the quiver diagram., Comment: 31 pages, 5 figures; v2: minor corrections, references added

It was shown in arXiv:2309.10786 that the leading non-perturbative contribution to the large $N$ expansion of superconformal index of (2,0) 6d theory (which describes low-energy dynamics of $N$ coincident M5 branes) is reproduced by the semiclassical partition function of quantum M2 brane wrapped on $S^{1}\times S^{2}$ in a twisted version of AdS$_{7}\times S^{4}$ background. Here we demonstrate an analogous relation for the leading non-perturbative contribution to the large $N$ expansion of the superconformal index of the ${n}=8$ supersymmetric level-one $U(N) \times U(N)$ ABJM theory (which describes low-energy dynamics of $N$ coincident M2 branes). The roles of M2 and M5 branes get effectively interchanged. Namely, the large $N$ correction to the ABJM index is found to be given by the semiclassical partition function of quantum M5 brane wrapped on $S^1 \times S^5$ in a twisted version of AdS$_{4}\times S^{7}$ background. This effectively confirms the suggestion for the "M5 brane index" made in arXiv:2007.05213 on the basis of indirect superconformal algebra considerations., Comment: 35 pages. v2: refs. added

The superconformal index $Z$ of the 6d (2,0) theory on $S^5 \times S^1$ (which is related to the localization partition function of 5d SYM on $S^5$) should be captured at large $N$ by the quantum M2 brane theory in the dual M-theory background. Generalizing the type IIA string theory limit of this relation discussed in arXiv:2111.15493 and arXiv:2304.12340, we consider semiclassically quantized M2 branes in a half-supersymmetric 11d background which is a twisted product of thermal AdS$_7$ and $S^4$. We show that the leading non-perturbative term at large $N$ is reproduced precisely by the 1-loop partition function of an "instanton" M2 brane wrapped on $S^1\times S^2$ with $S^2\subset S^4$. Similarly, the (2,0) theory analog of the BPS Wilson loop expectation value is reproduced by the partition function of a "defect" M2 brane wrapped on thermal AdS$_3\subset$ AdS$_7$. We comment on a curious analogy of these results with similar computations in arXiv:2303.15207 and arXiv:2307.14112 of the partition function of quantum M2 branes in AdS$_4 \times S^7/\mathbb Z_k$ which reproduced the corresponding localization expressions in the ABJM 3d gauge theory., Comment: 26 pages. v4: misprint corrected and footnote added

We show that the Bekenstein-Hawking entropy of large supersymmetric black holes in AdS$_5\times S^5$ emerges from remarkable cancellations in the giant graviton expansions recently proposed by Imamura, and Gaiotto and Lee, independently. A similar cancellation mechanism is shown to happen in the exact expansion in terms of free fermions recently put-forward by Murthy. These two representations can be understood as sums over independent systems of giant D3-branes and free fermions, respectively. At large charges, the free energy of each independent system localizes to its asymptotic expansion near the leading singularity. The sum over the independent systems maps their localized free energy to the localized free energy of the superconformal index of $U(N)$ $\mathcal{N}=4$ SYM. This result constitutes a non-perturbative test of the giant graviton expansion valid at any value of $N$. Moreover, in the holographic scaling limit $N\to\infty$ at fixed ratio $\frac{\text{Entropy}}{N^2}\,$, it recovers the 1/16 BPS black hole entropy by a saddle-point approximation of the giant graviton expansion., Comment: 55 pp, 1 fig; v2: refs added, typos corrected, matches version in journal

We present a quantum M2 brane computation of the instanton prefactor in the leading non-perturbative contribution to the ABJM 3-sphere free energy at large $N$ and fixed level $k$. Using supersymmetric localization, such instanton contribution was found earlier to take the form $F^{\rm inst}(N,k) = - ({\sin^{2} \frac{2\pi}{k}} )^{-1} \, \exp (-2\pi \sqrt\frac{2N}{k}) + \cdots$ . The exponent comes from the action of an M2 brane instanton wrapped on $S^3/{\mathbb Z}_k$, which represents the M-theory uplift of the $\mathbb{C}P^1$ instanton in type IIA string theory on AdS$_4 \times \mathbb{C}P^3$. The IIA string computation of the leading large $k$ term in the instanton prefactor was recently performed in arXiv:2304.12340. Here we find that the exact value of the prefactor $({\sin^{2} \frac{2\pi}{k}})^{-1} $ is reproduced by the 1-loop term in the M2 brane partition function expanded near the $S^3/\mathbb{Z}_k$ instanton configuration. As in the Wilson loop example in arXiv:2303.15207, the quantum M2 brane computation is well defined and produces a finite result in exact agreement with localization., Comment: 27 pages. v2: comments added

We compare large $N$ expansion of the localization result for the free energy $F$ in the 3d $\mathcal{N}=6$ superconformal $U(N)_k \times U(N)_{-k}$ Chern-Simons-matter theory to its AdS/CFT counterpart, i.e. to the perturbative expansion of M-theory partition function on AdS$_{4}\times S^{7}/\mathbb{Z}_{k}$ and to the weak string coupling expansion of type IIA effective action on AdS$_{4}\times {\rm CP}^3$. We show that the general form of the perturbative expansions of $F$ on the two sides of the AdS/CFT duality is indeed the same. Moreover, the transcendentality properties of the coefficients in the large $N$, large $k$ expansion of $F$ match those in the corresponding M-theory or string theory expansions. To shed light on the structure of the 1-loop M-theory partition function on AdS$_{4}\times S^{7}/\mathbb{Z}_{k}$ we use the expression for the 1-loop 4-graviton scattering amplitude in the 11d supergravity. We also use the known information about the transcendental coefficients of the leading curvature invariants in the low-energy effective action of type II string theory. Matching of the remaining rational factors in the coefficients requires a precise information about currently unknown RR field strength terms in the corresponding superinvariants., Comment: 24 pages. v3: comments added in Appendix B

We consider the Schur index of $\mathcal N=4$ $U(N)$ SYM theory in 4d and its holographic giant graviton-type expansion at finite $N$. We compute the world-volume brane superconformal index by a recently proposed definition of the gauge holonomy integral as a multivariate residue. This is evaluated by a novel deformation algorithm that avoids Gr\"obner basis methods. Various terms of the brane expansion are computed and shown to be free of wall-crossing singularities to the order we explored. The relation between the brane expansion and previous giant graviton-type represenations of the Schur index is clarified., Comment: 25 pages. v2: minor latex fix

We study the role of Quorum Sensing (QS) in the growth of bacterial colonies and in the bioluminescence produced. These two phenomena are both regulated by QS and the experimental data show a non-trivial correlation between them. It is also known that the specific bacterial substrate potentially modifies the behavior of the colony. In the specific case of the bioluminescent gram-negative bacterium, Vibrio harveyi, we propose a three-autoinducer model in which QS is described in terms of long-range interaction between charged objects placed on a regular network and playing the role of bacteria. The charges spread in the network through fictitious non-linear electrostatic interactions. QS is monitored by analyzing the current flowing within the network. The model parameters are determined by comparing the simulations with the data present in the literature and related to liquid cultures. New colony growth measurements are then performed on Vibrio campbelli (a member of the clade Harveyi) grown on hydroxyapatite (HA) substrates relevant for biomedical applications. Growth on the substrate differs from growth in liquid culture, although the observed bioluminescence is similar. We exploit our model to understand the differences between colonies in liquid culture and on substrate in terms of the relative role and cooperation of the three autoinducers., Comment: 8 pages, 5 figures

We study non-planar corrections in two special $\mathcal N=2$ superconformal $SU(N)$ gauge theories that are planar-equivalent to $\mathcal N=4$ SYM theory: two-nodes quiver model with equal couplings and $\mathcal N=2$ vector multiplet coupled to two hypermultiplets in rank-2 symmetric and antisymmetric representations. We focus on two observables in these theories that admit representation in terms of localization matrix model: free energy on 4-sphere and the expectation value of half-BPS circular Wilson loop. We extend the methods developed in arXiv:2207.11475 to derive a systematical expansion of non-planar corrections to these observables at strong 't Hooft coupling constant $\lambda$. We show that the leading non planar corrections are given by a power series in $\lambda^{3/2}/N^2$ with rational coefficients. Sending $N$ and the coupling constant $\lambda$ to infinity with $\lambda^{3/2}/N^2$ kept fixed corresponds to the familiar double scaling limit in matrix models. We find that in this limit the observables in the two models are related in a remarkably simple way: the free energies differ by the factor of $2$, whereas the Wilson loop expectation values coincide. Surprisingly, these relations hold only at strong coupling, they are not valid in the weak coupling regime. We also discuss a dual string theory interpretation of the leading corrections to the free energy in the double scaling limit suggesting their relation to curvature corrections in type IIB string effective action., Comment: 54 pages. v2: minor clarifications

We consider four dimensional $U(N)$ $\mathcal N=4$ SYM theory interacting with a 3d $\mathcal N=4$ theory living on a codimension-one interface and holographically dual to the D3-D5 system without flux. Localization captures several observables in this dCFT, including its free energy, related to the defect expectation value, and single trace $\frac{1}{2}$-BPS composite scalars. These quantities may be computed in a hermitian one-matrix model with non-polynomial single-trace potential. We exploit the integrable Volterra hierarchy underlying the matrix model and systematically study its $1/N$ expansion at any value of the 't Hooft coupling. In particular, the strong coupling regime is determined -- up to non-perturbative exponentially suppressed corrections -- by differential relations that constrain higher order terms in the $1/N$ expansion. The analysis is extended to the model with $SU(N)$ gauge symmetry by resorting to the more general Toda lattice equations., Comment: 39 pages. v2: extended bibliography

We apply the localization technique to compute the free energy on four-sphere and the circular BPS Wilson loop in the four-dimensional $\cal N$=2 superconformal $Sp(2N)$ gauge theory containing vector multiplet coupled to four hypermultiplets in fundamental representation and one hypermultiplet in rank-2 antisymmetric representation. This theory is unique among similar $\cal N$=2 superconformal models that are planar-equivalent to $\cal N$=4 SYM in that the corresponding localization matrix model has the interaction potential containing single-trace terms only. We exploit this property to show that, to any order in large $N$ expansion and an arbitrary 't Hooft coupling $\lambda$, the free energy and the Wilson loop satisfy Toda lattice equations. Solving these equations at strong coupling, we find remarkably simple expressions for these observables which include all corrections in $1/N$ and $1/\sqrt{\lambda}$. We also compute the leading exponentially suppressed ${\cal O}(e^{-\sqrt{\lambda}})$ corrections and consider a generalization to the case when the fundamental hypermultiplets have a non-zero mass. The string theory dual of this $\cal N$=2 gauge theory should be a particular orientifold of AdS$_5 \times S^5$ type IIB string and we discuss the string theory interpretation of the obtained strong-coupling results., Comment: 41 pages. v2: minor correction; v3: eqs.(2.41) and (2.43) corrected

We propose a model for bacterial Quorum Sensing based on an auxiliary electrostatic-like interac-tion originating from a fictitious electrical charge that represents bacteria activity. A cooperative mechanism for charge/activity exchange is introduced to implement chemotaxis and replication. The bacteria system is thus represented by means of a complex resistor network where link re-sistances take into account the allowed activity-flow among individuals. By explicit spatial sto-chastic simulations, we show that the model exhibits different quasi-realistic behaviors from colo-ny formation to biofilm aggregation. The electrical signal associated with Quorum Sensing is ana-lyzed in space and time and provides useful information about the colony dynamics. In particular, we analyze the transition between the planktonic and the colony phases as the intensity of Quorum Sensing is varied., Comment: 11 pages, 5 figures

We consider strong 't Hooft coupling expansion in special four-dimensional $\mathcal N=2$ superconformal models that are planar-equivalent to $\mathcal N=4$ super Yang-Mills theory. Various observables in these models that admit localization matrix model representation can be expressed at large $N$ in terms of a Fredholm determinant of a Bessel operator. The latter previously appeared in the study of level spacing distributions in matrix models and, more recently, in four-point correlation functions of infinitely heavy half-BPS operators in planar $\mathcal N=4$ SYM. We use this relation and a suitably generalized Szego-Akhiezer-Kac formula to derive the strong 't Hooft coupling expansion of the leading corrections to free energy, half-BPS circular Wilson loop, and certain correlators of chiral primaries operators in the $\mathcal N=2$ models. This substantially generalizes partial results in the literature and represents a challenge for dual string theory calculations in AdS/CFT context. We also demonstrate that the resulting strong-coupling expansions suffer from Borel singularities and require adding non-perturbative, exponentially suppressed corrections. As a byproduct of our analysis, we determine the non-perturbative correction to the above mentioned four-point correlator in planar $\mathcal N=4$ SYM., Comment: 65 pages. v2: misprints and eq.(4.20) corrected, note added; v3: minor clarifications