Question: In what year did Strominger and Vafa show their black hle theory?
About the article "Black hole", section "Entropy and thermodynamics".

Candidate passages:
He has collaborated with string theorists including Strominger, Vafa and Witten, and as post-doctorals from theoretical physics with B. Greene, E. Zaslow and A. Klemm .
The Strominger–Yau–Zaslow program is to construct explicitly mirror manifolds.
David Gieseker wrote of the seminal role of the Calabi conjecture in relating string theory with algebraic geometry, in particular for the developments of the SYZ program, mirror conjecture and Yau–Zaslow conjecture. 
Cumrun Vafa is a string theorist.
His research is focused on the nature of quantum gravity and the relation between geometry and quantum field theories.
He is known in the string theory community for his co-discovery, with Strominger, that the Bekenstein-Hawking entropy of a black hole can be accounted for by solitonic states of superstring theory, and for expounding the relation between geometry and field theories that arise through string dualities (culminating in the Gopakumar-Vafa conjecture).
This topic has been known as "geometric engineering of quantum field theories".
In 1997, he developed F-theory.
He is also interested in understanding the underlying meaning of string dualities, as well as trying to apply superstring theory to some unsolved questions of elementary particle physics such as the hierarchy problem and the cosmological constant problem.
He has had profound contributions to topological string theories and to the understanding of mirror symmetry.
He is also a trustee of Network of Iranians for Knowledge and Innovation (NIKI).required 
Andrew Eben Strominger (born 1955) is an American theoretical physicist who works on string theory and son of Jack L. Strominger.
He is currently a professor at Harvard University and a senior fellow at the Society of Fellows.
He attended the Cambridge School of Weston for high school, and received his undergraduate degree from Harvard University in 1977, and his Ph.D from the Massachusetts Institute of Technology in 1982 under the supervision of Roman Jackiw.
His contributions to physics include:  a paper with Cumrun Vafa that explains the microscopic origin of the black hole entropy, originally calculated thermodynamically by Stephen Hawking and Jacob Bekenstein, from string theory  a paper with Philip Candelas, Gary Horowitz, and Edward Witten in the 1980s about the relevance of Calabi-Yau manifolds for obtaining the Standard Model from string theory  other articles discussing the dS/CFT correspondence (a variation of AdS/CFT correspondence); S-branes (a variation of D-branes)  OM-theory (with Shiraz Minwalla and Nathan Seiberg)  noncommutative solitons (with Shiraz Minwalla and Rajesh Gopakumar)  massless black holes in the form of wrapped D3-branes that regulate the physics of a conifold and allow topology change  interpretation of mirror symmetry as a special case of T-duality (with Eric Zaslow and Shing-Tung Yau)  purely cubic action for string field theory  superstrings with torsion  
In that same year the nations with the highest HLE were:  Iceland  Netherlands  Sweden  Switzerland  Austria The USA ranked 10th on the 1996 HLE scale. 
The only way to satisfy the second law of thermodynamics is to admit that black holes have entropy.
If black holes carried no entropy, it would be possible to violate the second law by throwing mass into the black hole.
The increase of the entropy of the black hole more than compensates for the decrease of the entropy carried by the object that was swallowed.
Starting from theorems proved by Stephen Hawking, Jacob Bekenstein conjectured that the black hole entropy was proportional to the area of its event horizon divided by the Planck area.
Bekenstein suggested formula_1 as the constant of proportionality, asserting that if the constant was not exactly this, it must be very close to it.
The next year, Hawking showed that black holes emit thermal Hawking radiation corresponding to a certain temperature (Hawking temperature).
Using the thermodynamic relationship between energy, temperature and entropy, Hawking was able to confirm Bekenstein's conjecture and fix the constant of proportionality at formula_2: formula_3 where formula_4 is the area of the event horizon, calculated at formula_5, formula_6 is Boltzmann's constant, and formula_7 is the Planck length.
This is often referred to as the Bekenstein–Hawking formula.
The subscript BH either stands for "black hole" or "Bekenstein-Hawking".
The black hole entropy is proportional to the area of its event horizon formula_4.
The fact that the black hole entropy is also the maximal entropy that can be obtained by the Bekenstein bound (wherein the Bekenstein bound becomes an equality) was the main observation that led to the holographic principle.
Although Hawking's calculations gave further thermodynamic evidence for black hole entropy, until 1995 no one was able to make a controlled calculation of black hole entropy based on statistical mechanics, which associates entropy with a large number of microstates.
In fact, so called "no hair" theorems appeared to suggest that black holes could have only a single microstate.
The situation changed in 1995 when Andrew Strominger and Cumrun Vafa calculated the right Bekenstein-Hawking entropy of a supersymmetric black hole in string theory, using methods based on D-branes and string duality.
Their calculation was followed by many similar computations of entropy of large classes of other extremal and near-extremal black holes, and the result always agreed with the Bekenstein-Hawking formula.
However, for Schwarzschild black hole, viewed as the most far from the extremal black hole, the relationship between micro and macro-state is expected to be clarified from the string theoretical viewpoint.
Various studies are in progress, but has not been elucidated.
In Loop quantum gravity (LQG) it is possible to associate a geometrical interpretation to the microstates: these are the quantum geometries of the horizon.
LQG offers a geometric explanation of the finiteness of the entropy and of the proportionality of the area of the horizon.
It is possible to derive, from the covariant formulation of full quantum theory (Spinfoam) the correct relation between energy and area (1st law), the Unruh temperature and the distribution that yields Hawking entropy.
The calculation makes use of the notion of dynamical horizon and is done for non-extremal black holes.
There seems to be also discussed the calculation of Beckenstein-Hawking entropy from the point of view of LQG.