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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeJun 30th 2013

    added a bit more text to the Idea-section at Wick rotation and in particular added cross-links with Osterwalder-Schrader theorem.

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeNov 9th 2018

    added an overview-diagram to the Idea section (copied over from Euclidean field theory)

    diff, v17, current

    • CommentRowNumber3.
    • CommentAuthorDavid_Corfield
    • CommentTimeNov 9th 2018

    Does this Wick rotation story ’lift’ to some relation between stable cohomotopy spaces?

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeNov 9th 2018
    • (edited Nov 9th 2018)

    Right, so by the discussion at stable splitting of mapping spaces we have that the real cohomology of the space of spatially compactly supported cocycles in degree-4 cohomotopy on Minkowski spacetime (“Lorentzian instantons”) is equivalently correlators of Euclidean field theory on R 3×S 1R^3 \times S^1, hence Is Wick-rotated n-point functions of relativistic field theory on Minkowski spacetime at finite temperature.

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeNov 10th 2018

    added a few more words to the Idea-section, and pointed more prominently to Fulling-Ruijsenaars 87

    diff, v20, current

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeNov 10th 2018
    • (edited Nov 10th 2018)

    added picture of the rotation doing it’s thing

    diff, v21, current

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeApr 19th 2021

    added these pointers:

    On the (non-)existence of Wick rotation for quantum field theory on curved spacetimes:

    MathOverflow comments:

    See also:

    diff, v24, current

    • CommentRowNumber8.
    • CommentAuthorUrs
    • CommentTimeDec 10th 2021
    • (edited Dec 10th 2021)

    added pointer to the recent writeup:

    and this recent talk:

    • Graeme Segal, Wick Rotation and the Positivity of Energy in Quantum Field Theory, talk at IAS Physics Group Meeting, December 2021 (video recording)

    following up on talks revolving around the same idea, such as

    • Graeme Segal, Wick rotation and the positivity of energy in quantum field theory, talk at Institut des Hautes Études Scientifiques (IHÉS), June 2014 (video recording)

    which the entry already used to be linking to.

    diff, v25, current

    • CommentRowNumber9.
    • CommentAuthorUrs
    • CommentTimeNov 16th 2023
    • (edited Nov 16th 2023)

    added publication data to this item:

    diff, v26, current

    • CommentRowNumber10.
    • CommentAuthorperezl.alonso
    • CommentTimeJan 26th 2024
    • (edited Jan 26th 2024)

    Is it known to some degree of rigour what happens to a BPS state under Wick rotation? In general, there are different allowed forms of supersymmetries depending on the signature of spacetime. In Section 4 of 2208.02267, it is briefly claimed that if one Wick rotates a 4d theory on a 2+22+2 signature (where the corresponding Spin group exhibits the exceptional isomorphism Spin(2,2)SL(2,)×SL(2,)\text{Spin}(2,2)\cong SL(2,\mathbb{R})\times SL(2,\mathbb{R})) to a 3+13+1 signature, one does not have a supersymmetric theory anymore, yet there are supposed to be states protected against radiative corrections. I’m wondering if this can be used to obtain additional states not manifestly protected in string theory by looking at BPS states on, for example, the analogues in other signatures.

    • CommentRowNumber11.
    • CommentAuthorUrs
    • CommentTimeJan 26th 2024

    Why do you say “yet” in “yet there are supposed to be states protected against radiative corrections”?

    It sounds like you are tacitly assuming that radiative corrections is something only seen after Wick rotation?

    Concerning your main question:

    I don’t know (how BPS states appear after Wick rotation).

    Generally, Wick rotation of non-trivial fields (notably spinors) is a subtle busines; I’d be surprised if the community that typically cares about BPS states has been careful enough to sort out their Wick rotation.