On TTˉT\bar{T} deformations and supersymmetry

We investigate the "$T\bar{T}$" deformations of two-dimensional supersymmetric quantum field theories. More precisely, we show that, by using the conservation equations for the supercurrent multiplet, the $T\bar{T}$ deforming operator can be constructed as a supersymmetric descendant. Here we focus on $\mathcal{N}=(1,0)$ and $\mathcal{N}=(1,1)$ supersymmetry. As an example, we analyse in detail the $T\bar{T}$ deformation of a free $\mathcal{N}=(1,0)$ supersymmetric action. We also argue that the link between $T\bar{T}$ and string theory can be extended to superstrings: by analysing the light-cone gauge fixing for superstrings in flat space, we show the correspondence of the string action to the $T\bar{T}$ deformation of a free theory of eight $\mathcal{N}=(1,1)$ scalar multiplets on the nose. We comment on how these constructions relate to the geometrical interpretations of $T\bar{T}$ deformations that have recently been discussed in the literature.Comment: V3: comments, references, and a new subsection 2.5 added; version to appear in JHEP; 29 page

Exact correlation functions in SU(2) N=2 superconformal QCD

We report an exact solution of 2- and 3-point functions of chiral primary fields in SU(2) N=2 super-Yang-Mills theory coupled to four hypermultiplets. It is shown that these correlation functions are non-trivial functions of the gauge coupling, obeying differential equations which take the form of the semi-infinite Toda chain. We solve these equations recursively in terms of the Zamolodchikov metric that can be determined exactly from supersymmetric localization on the four-sphere. Our results are verified independently in perturbation theory with a Feynman diagram computation up to 2-loops. This is a short version of a companion paper that contains detailed technical remarks, additional material and aspects of an extension to SU(N) gauge group.Comment: 5 page

The Role of Diverse Strategies in Sustainable Knowledge Production

Online communities are becoming increasingly important as platforms for large-scale human cooperation. These communities allow users seeking and sharing professional skills to solve problems collaboratively. To investigate how users cooperate to complete a large number of knowledge-producing tasks, we analyze StackExchange, one of the largest question and answer systems in the world. We construct attention networks to model the growth of 110 communities in the StackExchange system and quantify individual answering strategies using the linking dynamics of attention networks. We identify two types of users taking different strategies. One strategy (type A) aims at performing maintenance by doing simple tasks, while the other strategy (type B) aims investing time in doing challenging tasks. We find that the number of type A needs to be twice as big as type B users for a sustainable growth of communities.Comment: 10 pages, 3 figure

Decoding a Three-Dimensional Conformal Manifold

We study the one-dimensional complex conformal manifold that controls the infrared dynamics of a three-dimensional $\mathcal{N}=2$ supersymmetric theory of three chiral superfields with a cubic superpotential. Two special points on this conformal manifold are the well-known XYZ model and three decoupled copies of the critical Wess-Zumino model. The conformal manifold enjoys a discrete duality group isomorphic to $S_4$ and can be thought of as an orbifold of $\mathbf{CP}^1$. We use the $4-\varepsilon$ expansion and the numerical conformal bootstrap to calculate the spectrum of conformal dimensions of low-lying operators and their OPE coefficients, and find a very good quantitative agreement between the two approaches.Comment: 59 pages, 13 figure

Higher Derivative Corrections and Central Charges from Wrapped M5-branes

We compute four-derivative corrections to the AdS supergravity actions arising from the near-horizon geometry of N M5-branes wrapped on either one or two Riemann surfaces. This setup features the novel presence of both gauged isometries as well as nontrivial hypermultiplets. We argue that the 5d Chern-Simons terms receive not only higher-derivative corrections but also contributions from Killing vector parameters, which we find must also be corrected. We check the central charges found by our supergravity methods against the dual field theory results and find perfect agreement at leading and subleading order in N. Along the way, we find higher derivative corrections to general AdS_5 and AdS_3x\Sigma_g geometries.Comment: 32 pages + 16 pages appendice

Modeling population dynamics of online communities

Online communities are more dynamic in terms of composition compared to traditional physical communities. This can affect the conditions for cooperation. We discuss empirical results from online communities and extend the evolution of firms model of Axtell to discover the conditions of cooperation in groups

Análise da formação de carteiras de investimentos: uma aplicação no mercado acionário brasileiro.

O objetivo deste estudo é verificar a capacidade dos modelos financeiros teóricos de gestão de carteiras, em subsidiar a obtenção de retornos anormais no mercado acionário brasileiro. Entre os modelos que se podem citar: o modelo de Gestão de Carteiras de Markowitz (1952), o modelo CAPM de Sharpe (1964), Lintner (1965) e Black (1972). Os resultados comprovam que os dois modelos testados conseguiram gerar rentabilidades anormais, se comparadas com o IBOVESPA no mesmo período e com uma variância inferior. O Índice de Sharpe (1966) apontou a carteira de Markowitz como a que obteve a melhor performance. Our objective is to assess the ability of theoretical models of financial portfolio management, in support to obtain abnormal returns in the Brazilian equity market. Among the models that may be cited: the model of portfolio management of Markowitz (1952), the CAPM of Sharpe (1964), Lintner (1965) and Black (1972). The results show that the two models tested successfully generate abnormal returns compared to the IBOVESPA in the same period and a lower variance. The index of Sharpe (1966) identified the portfolio of Markowitz as that achieved the best performance.Gestão de Carteiras, Mercado Acionário Brasileiro e Investimento em Renda Variável. Management Portfolios, Brazilian Stock Market and Investment in variable income.

Anomalous Breaking of Anisotropic Scaling Symmetry in the Quantum Lifshitz Model

In this note we investigate the anomalous breaking of anisotropic scaling symmetry in a non-relativistic field theory with dynamical exponent z=2. On general grounds, one can show that there exist two possible "central charges" which characterize the breaking of scale invariance. Using heat kernel methods, we compute these two central charges in the quantum Lifshitz model, a free field theory which is second order in time and fourth order in spatial derivatives. We find that one of the two central charges vanishes. Interestingly, this is also true for strongly coupled non-relativistic field theories with a geometric dual described by a metric and a massive vector field.Comment: 26 pages; major revision (results were unaffected), published versio