Is there confirmation in the text of sexual relations between Lord and Lady Macbeth in Macbeth? I want to know more about the intimate relations...

The simplest answer to your question is that, if you are
looking for confirmation in the play Macbeth, written by William
Shakespeare, for any sort of sexual activity between Lord and Lady Macbeth, you are out
of luck.  Shakespeare provides absolutely no suggestion of even a kiss between them.  I
notice that you are a doctorate student, so I assume that you are interested in rigorous
scrutiny of the text rather than conjecture.

A work of
literature is always simply the words that exist on the page.  Many authors are
wonderful at ambiguity and suggestion of possible thoughts or actions not directly
stated on the page, but you are much more likely to find this sort of device in a novel
or short story than in a play.  A play, of necessity, can't really present one
character's "internal life."  If it is said or spoken, it exists in the world of the
play, out in the open, and not in a character's mind. This is doubly true for
Shakespeare, who did not live and work in the world of Modern Drama with it's subtext
and isolating "fourth wall."

The modern idea of "subtext"
is a dramatic concept far removed from the dramatic conventions of Shakespeare's day. 
Characters in Shakespeare's plays, unless obviously deceiving another character, say
what they mean and mean what they say. Shakespeare does make excellent use of the
soliloquy, in which characters confide their secret intents or personal dilemmas to the
audience.  But this was also a "public" act for the character, since the audience was
considered as much a part of the play as any actor.  There was no sense of the "fourth
wall" which renders an audience "invisible" to the actors on the
stage.

Why go on and on about the differences between the
world of theatre in Shakespeare's day and our own modern one?  Simply because it is in
the modern treatment of his plays, including Macbeth, that you will
find additions that provide touches like the indication of "sexual relations" between
Lord and Lady Macbeth.

Please remember that a script, even
the superior scripts written by Shakespeare, are only part of the story.  They are the
words spoken by the characters.  The action of the play is created but the theatre
company (or film company) producing it.  So, whether there is any sort of romantic or
sexual interaction between Lord and Lady Macbeth is something that you will notice
differs from production to production, not something set in the script by
Shakespeare.

You could certainly pursue the question you
ask as it relates to different productions of the play.  Film versions that you could
compare in this regard are the Macbeths of Orson Welles, Roman
Polanski and Geoffrey Wright.  Compare the way each of these filmmakers presents the
sexual relationship between the main characters.

For more
on performed versions of the play, please follow the links
below.