Theories in two space-time dimensions provide playground for exploring geometry of the "Theory Space" - the collection of all quantum field theories. Recently introduced "TTbar deformations" of 2D quantum field theories bring insight into the structure of that space. These are special deformations, "irrelevant" in the renormalization group sense and thus likely altering the local structure of the theory. At the same time, the TTbar deformations generate robust and even solvable theories. Of special interest are the deformations of integrable field theories, where they can be related to deformations of the associated factorizable S-matrix, and the theory can be treated using the powerful tool of the Thermodynamic Bethe ansatz. Preliminary results suggest that the deformed theories typically develop Hagedorn-like density of states, similar to that in the string theories.
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