Mass formulas for multicenter BPS 4D black holes are presented. In the case of two center BPS solutions, the ADM mass can be related to the intercenter distance r, the angular momentum J2, the dyonic ...charge vectors qi and the value of the scalar moduli at infinity (z∞)by the Smarr-like expressionMADM2=A(1+αJ2(1+2MADM/r+A/r2)) where A(Q),α(qi) are symplectic invariant quantities (Q, the total charge vector) depending on the special geometry prepotential defining the theory. The formula predicts the existence of a continuos class, for fixed value of the charges, of BH's with interdistances r∈(0,∞) and MADM∈(∞,M∞). First Law expressions incorporating the intercenter distance are obtained from it:dM≡ΩdJ+Φidqi+Fdr, in addition to an effective angular velocity Ω and electromagnetic potentials Φi, the equation allows to define an effective “force”, F, acting between the centers. This effective force is always negative: at infinity and at short distances we recover the familiar Newton law F∼1/r2 at the leading order. Similar results can be easily obtained for more general models and number of centers.
We study the shadow behaviors of five dimensional (5D) black holes embedded in type IIB superstring/supergravity inspired spacetimes by considering solutions with and without rotations. Geometrical ...properties as shapes and sizes are analyzed in terms of the D3-brane number and the rotation parameter. Concretely, we find that the shapes are indeed significantly distorted by such physical parameters and the size of the shadows decreases with the brane or “color” number and the rotation. Then, we investigate geometrical observables and energy emission rate aspects.
A general method to build the entanglement renormalization (cMERA) for interacting quantum field theories is presented. We improve upon the well-known Gaussian formalism used in free theories through ...a class of variational non-Gaussian wave functionals for which expectation values of local operators can be efficiently calculated analytically and in a closed form. The method consists of a series of scale-dependent nonlinear canonical transformations on the fields of the theory under consideration. Here, the λϕ4 and the sine-Gordon scalar theories are used to illustrate how nonperturbative effects far beyond the Gaussian approximation are obtained by considering the energy functional and the correlation functions of the theory.
A
bstract
We study General Freudenthal Transformations (GFT) on black hole solutions in Einstein-Maxwell-Scalar (super)gravity theories with global symmetry of type
E
7
. GFT can be considered as a ...2-parameter,
a, b
∈ ℝ, generalisation of Freudenthal duality:
x
→
x
F
=
ax
+
b
x
˜
, where
x
is the vector of the electromagnetic charges, an element of a Freudenthal triple system (FTS), carried by a large black hole and
x
˜
is its Freudenthal dual. These transformations leave the Bekenstein-Hawking entropy invariant up to a scalar factor given by
a
2
±
b
2
. For any
x
there exists a one parameter subset of GFT that leave the entropy invariant,
a
2
±
b
2
= 1, defining the subgroup of Freudenthal rotations. The Freudenthal plane defined by span
ℝ
{
x,
x
˜
} is closed under GFT and is foliated by the orbits of the Freudenthal rotations. Having introduced the basic definitions and presented their properties in detail, we consider the relation of GFT to the global symmetries or U-dualities in the context of supergravity. We consider explicit examples in pure supergravity, axion-dilaton theories and
N
= 2
, D
= 4 supergravities obtained from
D
= 5 by dimensional reductions associated to (non-degenerate) reduced FTS’s descending from cubic Jordan Algebras.
A
bstract
We present a detailed description of
N
= 2 stationary BPS multicenter black hole solutions for quadratic prepotentials with an arbitrary number of centers and scalar fields making a ...systematic use of the algebraic properties of the matrix of second derivatives of the prepotential,
, which in this case is a scalar-independent matrix. In particular we obtain bounds on the physical parameters of the multicenter solution such as horizon areas and ADM mass. We discuss the possibility and convenience of setting up a basis of the symplectic vector space built from charge eigenvectors of the
, the set of vectors (P
±
q
a
) with P
±
-eigenspace projectors.
The anti-involution matrix
can be understood as a Freudenthal duality
. We show that this duality can be generalized to “Freudenthal transformations”
under which the horizon area, ADM mass and intercenter distances scale up leaving constant the scalars at the fixed points. In the special case λ = 1, “
-rotations”, the transformations leave invariant the solution. The standard Freudenthal duality can be written as
.
We argue that these generalized transformations leave invariant not only the quadratic prepotential theories but also the general stringy extremal quartic form Δ
4
, Δ
4
(
x
) = Δ
4
(cos
θx
+ sin
θ
) and therefore its entropy at lowest order.
On the light of the recent LHC boson discovery, we present a phenomenological evaluation of the ratio ρt = mZmt/m2H, from the LHC combined mH value, we get ((1σ)) This value is close to one with a ...precision of the order ∼ 1%. Similarly we evaluate the ratio ρWt = (mW + mt)/(2mH). From the up-to-date mass values we get ρ(exp)wt = 1.0066 ± 0.0035 (1σ). The Higgs mass is numerically close (at the 1% level) to the mH ∼ (mW + mt)/2. From these relations we can write any two mass ratios as a function of, exclusively, the Weinberg angle (with a precision of the order of 1% or better):(1) For example: mH/mZ ≃ 1 + √2s2θW/2, mH/mtcθW ≃ 1 − √2s2θW/2. In the limit cos θW → 1 all the masses would become equal mZ = mW = mt = mH. It is tempting to think that such a value, it is not a mere coincidence but, on naturalness grounds, a signal of some more deeper symmetry. In a model independent way, ρt can be viewed as the ratio of the highest massive representatives of the spin (0, 1/2, 1) SM and, to a very good precision the LHC evidence tell us that ms=1ms=1/2/m2s=0 ≃ 1. Somehow the “lowest” scalar particle mass is the geometric mean of the highest spin 1, 1/2 masses. We review the theoretical situation of this ratio in the SM and beyond. In the SM these relations are rather stable under RGE pointing out to some underlying UV symmetry. In the SM such a ratio hints for a non-casual relation of the type λ ≃ κ(g2 + g′2) with κ ≃ 1 + o(g/gt). Moreover the existence of relations mi/mj ≃ fij(θW) could be interpreted as a hint for a role of the SU(2)c custodial symmetry, together with other unknown mechanism. Without a symmetry at hand to explain then in the SM, it arises a Higgs mass coincidence problem, why the ratios ρt, ρWt are so close to one, can we find a mechanism that naturally gives m2H = mZmt, 2mH = mW + mt ?. PACS:14.80.Bn,14.80.Cp.
We construct the most general maximal gauged/massive supergravity in d = 9 dimensions and determine its extended field content by using the embedding tensor method.
The Higgs mass coincidence problem Torrente-Lujan, E.
Nuclear and particle physics proceedings,
April-June 2016, 2016-04-00, Letnik:
273-275
Journal Article
Recenzirano
Odprti dostop
We present a phenomenological evaluation of the ratio ρt=mZmt/mH2, from the LHC combined mH value, we get ((1σ))ρt(exp)=0.9956±0.0081. This value is close to one with a precision of the order ∼ 1%. ...Similarly we evaluate the ratio ρWt=(mW+mt)/(2mH). From the up-to-date mass values we get ρWt(exp)=1.0066±0.0035(1σ). The Higgs mass is numerically close (at the 1% level) to the mH∼(mW+mt)/2. From these relations we can write any two mass ratios as a function of, exclusively, the Weinberg angle (with a precision of the order of 1% or better):(1)mimj≃fij(θW),i,j=W,Z,H,t. For example: mH/mZ≃1+2sθW/22, mH/mtcθW≃1−2sθW/22. In the limit cosθW→1 all the masses would become equal mZ=mW=mt=mH.
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